tag:blogger.com,1999:blog-61148368587659817392024-02-06T21:30:31.757-08:00EdnaldoMatemátic@Unknownnoreply@blogger.comBlogger374125tag:blogger.com,1999:blog-6114836858765981739.post-9967769265650116042023-08-22T17:37:00.002-07:002023-08-24T17:02:46.130-07:00<p><b><u> PERÍMETRO E ÁREA DE FIGURAS - 6 ANO</u></b></p><p><span style="font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="system-ui"><span style="font-size: 12pt;">1.) </span></span></span></span><span style="font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="system-ui"><span style="font-size: 12pt;">Qual</span></span></span></span><strong><span style="font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="system-ui"><span style="font-size: 12pt;"><span style="font-weight: normal;"> </span></span></span></span></span></strong><span style="font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="system-ui"><span style="font-size: 12pt;">a área e o perímetro de um campo de futebol, de base 25 m e altura 5 m?</span></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="color: black;"><span face="system-ui"><span style="font-size: 12pt;">a) A= 100m², P= 50m b) A= 150 m², P= 60m</span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="color: black;"><span face="system-ui"><span style="font-size: 12pt;">c) A= 125 m², P= 60 m d) A= 120 m², P= 50 m</span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.25cm;"><br /><br /></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="color: black;"><span face="system-ui"><span style="font-size: 12pt;">2.) <span style="font-size: 12pt;">Definimos como perímetro:</span></span></span></span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span style="color: black;"><span face="system-ui"><span style="font-size: 12pt;"><br /></span></span></span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span style="color: black;"><span face="system-ui"><span style="font-size: 12pt;">a) a medida da superfície de uma figura plana.</span></span></span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span face="system-ui" style="font-size: 12pt;">b) a capacidade de um sólido geométrico.</span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span style="color: black;"><span face="system-ui"><span style="font-size: 12pt;">c) o comprimento de uma das dimensões de uma figura plana.</span></span></span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span style="color: black;"><span face="system-ui"><span style="font-size: 12pt;">d) o comprimento do contorno de uma figura plana.</span></span></span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span style="color: black;"><span face="system-ui"><span style="font-size: 12pt;">e) o espaço ocupado por um sólido geométrico.</span></span></span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span style="color: black;"><span face="system-ui"><span style="font-size: 12pt;"><br /></span></span></span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span face="system-ui" style="font-size: 16px;">3.) Em </span><span face="system-ui" style="background-color: transparent; font-size: 12pt;">um forro de mesa que possui 1,10 m de largura e 1,40 metros de </span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span face="system-ui" style="background-color: transparent; font-size: 12pt;"> comprimento </span><span face="system-ui" style="background-color: transparent; font-size: 12pt;">será feito um </span><span face="system-ui" style="background-color: transparent; font-size: 12pt;">bordado. Em quantos metros desse forro </span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span face="system-ui" style="background-color: transparent; font-size: 12pt;"> de mesa, </span><span face="system-ui" style="background-color: transparent; font-size: 12pt;">no mínimo, </span><span face="system-ui" style="background-color: transparent; font-size: 12pt;">foi feito esse </span><span style="background-color: transparent; font-size: 12pt;">bordado?</span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span face="system-ui" style="background-color: transparent; font-size: 12pt;"> </span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span face="system-ui" style="font-size: 12pt;"><br /></span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span face="system-ui" style="font-size: 12pt;">a) 1 metro</span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span style="color: black;"><span face="system-ui"><span style="font-size: 12pt;">b) 2 metros</span></span></span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span style="color: black;"><span face="system-ui"><span style="font-size: 12pt;">c) 3 metros</span></span></span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span style="color: black;"><span face="system-ui"><span style="font-size: 12pt;">d) 4 metros</span></span></span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span style="color: black;"><span face="system-ui"><span style="font-size: 12pt;">e) 5 metros </span></span></span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span style="color: black;"><span face="system-ui"><span style="font-size: 12pt;"><br /></span></span></span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span style="color: black;"><span face="system-ui"><span style="font-size: 12pt;">4.) </span></span></span><span face="system-ui" style="background-color: transparent; font-size: 12pt;">A tela de um televisor está em uma razão de 4 para 3. Se o perímetro do </span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span face="system-ui" style="background-color: transparent; font-size: 12pt;"> televisor </span><span face="system-ui" style="background-color: transparent; font-size: 12pt;">é de 280 </span><span style="background-color: transparent; font-size: 12pt;">cm, então ele possui área igual a:</span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span style="color: black;"><span face="system-ui"><span style="font-size: 12pt;"><br /></span></span></span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span style="color: black;"><span face="system-ui"><span style="font-size: 12pt;">a) 3600 cm²</span></span></span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span style="color: black;"><span face="system-ui"><span style="font-size: 12pt;">b) 4800 cm²</span></span></span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span style="color: black;"><span face="system-ui"><span style="font-size: 12pt;">c) 5400 cm²</span></span></span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span style="color: black;"><span face="system-ui"><span style="font-size: 12pt;">d) 6200 cm²</span></span></span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span style="color: black;"><span face="system-ui"><span style="font-size: 12pt;">e) 6400 cm² </span></span></span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span style="color: black;"><span face="system-ui"><span style="font-size: 12pt;"><br /></span></span></span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span style="color: black;"><span face="system-ui"><span style="font-size: 12pt;">5.) </span></span></span><span face="system-ui" style="background-color: transparent; font-size: 12pt;">Durante um treino de futebol, o técnico pediu para que </span><span face="system-ui" style="background-color: transparent; font-size: 12pt;">os jogadores </span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span face="system-ui" style="background-color: transparent; font-size: 12pt;">dessem </span><span face="system-ui" style="background-color: transparent; font-size: 12pt;">12 voltas correndo em torno do gramado. </span><span face="system-ui" style="background-color: transparent; font-size: 12pt;">Sabendo que o campo </span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span face="system-ui" style="background-color: transparent; font-size: 12pt;">possui 98 metros de </span><span style="background-color: transparent; font-size: 12pt;">largura e 72 metros de comprimento, a distância </span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span style="background-color: transparent; font-size: 12pt;">percorrida </span><span style="background-color: transparent; font-size: 12pt;">pelos atletas foi igual a:</span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span style="color: black;"><span face="system-ui"><span style="font-size: 12pt;"><br /></span></span></span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span style="color: black;"><span face="system-ui"><span style="font-size: 12pt;">a) 4080 m </span></span></span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span style="color: black;"><span face="system-ui"><span style="font-size: 12pt;">b) 2040 m </span></span></span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span style="color: black;"><span face="system-ui"><span style="font-size: 12pt;">c) 1020 m </span></span></span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span style="color: black;"><span face="system-ui"><span style="font-size: 12pt;">d) 510 m </span></span></span></p><p style="background: rgb(255, 255, 255); border: none; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span style="color: black;"><span face="system-ui"><span style="font-size: 12pt;">e) 340 m</span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1.15px; margin-bottom: 0cm;"><br /></p>Unknownnoreply@blogger.comtag:blogger.com,1999:blog-6114836858765981739.post-600578740716189092023-05-03T07:04:00.003-07:002023-05-03T07:04:47.366-07:00<p><u><b><span style="font-family: helvetica; font-size: medium;"> ALUNOS DESTAQUES I UNIDADE 2023 - CSM</span></b></u></p>
<p style="line-height: 100%; margin-bottom: 0cm;"><b><span style="color: red;"><u>GEOMETRIA</u></span></b></p>
<p style="line-height: 100%; margin-bottom: 0cm;"><b>6A – FERNANDA</b></p>
<p style="line-height: 100%; margin-bottom: 0cm;"><b>6B - MARIA
EDUARDA</b></p>
<p style="line-height: 100%; margin-bottom: 0cm;"><b>7A- IZABELA DINIZ</b></p>
<p style="line-height: 100%; margin-bottom: 0cm;"><b>8B – LARISSA
VITÓRIA</b></p>
<p style="line-height: 100%; margin-bottom: 0cm;"><b><span style="color: red;">MATEMÁTICA </span></b>
</p>
<p style="line-height: 100%; margin-bottom: 0cm;"><br />
</p>
<p style="line-height: 100%; margin-bottom: 0cm;"><b>6A– DANIELLE</b></p>
<p style="line-height: 100%; margin-bottom: 0cm;"><b>6B – JOÃO
VITOR</b></p>
<p style="line-height: 100%; margin-bottom: 0cm;"><b>7A – IZABELA
DINIZ</b></p>
<p style="line-height: 100%; margin-bottom: 0cm;"><b>7B – MARIA
SOFIA FALCÃO</b></p>
<p style="line-height: 100%; margin-bottom: 0cm;"><b>8A - GABRIELA
DINIZ</b></p>
<p style="line-height: 100%; margin-bottom: 0cm;"><b>1<sup>O </sup>
E.M – CAIO GOMES</b></p>
<p style="line-height: 100%; margin-bottom: 0cm;"><b>2<sup>O </sup>
E.M – MARIA VICTÓRIA MONTEIRO</b></p>
<p style="line-height: 100%; margin-bottom: 0cm;"><b>3<sup>O </sup>
E.M – NATÁLIA CLEMENTE </b>
</p>Unknownnoreply@blogger.comtag:blogger.com,1999:blog-6114836858765981739.post-76032530407554505852023-02-06T09:58:00.006-08:002023-02-06T10:00:03.028-08:00<p><b> MAIS UM ANO LETIVO SE INICIA, SEJAM BEM VINDOS</b></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiF-ErqQsIkuI_WNQwIXhxxauJ2-6TD1wC9xAjqYX5j1KDuqhqOTelTxjXGojrhd-wjbptr4rBl3XCZ_9gnFYgc06qnNkQZMFhDWk8amL_39gst560QdbMUQ-wP1QOrExPkwYX9Q00K9OOO0TwgIh0-bu9F_TqeBPkrjNXhx03qOZwGYRPQXbxzGi4l" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="334" data-original-width="500" height="323" src="https://blogger.googleusercontent.com/img/a/AVvXsEiF-ErqQsIkuI_WNQwIXhxxauJ2-6TD1wC9xAjqYX5j1KDuqhqOTelTxjXGojrhd-wjbptr4rBl3XCZ_9gnFYgc06qnNkQZMFhDWk8amL_39gst560QdbMUQ-wP1QOrExPkwYX9Q00K9OOO0TwgIh0-bu9F_TqeBPkrjNXhx03qOZwGYRPQXbxzGi4l=w580-h323" width="580" /></a></div><br /><p></p>Unknownnoreply@blogger.comtag:blogger.com,1999:blog-6114836858765981739.post-91574756427375612972022-05-25T17:41:00.000-07:002022-05-25T17:41:02.395-07:00ALUNO DESTAQUE DA I UNIDADE 2022<p>
</p><p align="center" style="font-style: normal; font-variant: normal; letter-spacing: normal; line-height: 0.79cm; margin-bottom: 0cm; orphans: 2; widows: 2;">
<span style="color: black;"><span style="font-family: Dyuthi;"><span style="font-size: xx-large;"><u><b><span style="background: transparent;">ALUNO
DESTAQUE 1ª UNIDADE 2022</span></b></u></span></span></span></p>
<p style="font-style: normal; font-variant: normal; letter-spacing: normal; line-height: 100%; margin-bottom: 0cm; orphans: 2; widows: 2;">
<br />
</p>
<p align="center" style="font-style: normal; font-variant: normal; letter-spacing: normal; line-height: 100%; margin-bottom: 0cm; orphans: 2; widows: 2;">
<span style="color: #f10d0c;"><span style="font-family: FreeSans, sans-serif;"><span style="font-size: xx-large;"><u><b>GEOMETRIA</b></u></span></span></span></p>
<p align="center" style="font-style: normal; font-variant: normal; letter-spacing: normal; line-height: 100%; margin-bottom: 0cm; orphans: 2; widows: 2;">
<br />
</p>
<p style="font-style: normal; font-variant: normal; letter-spacing: normal; line-height: 100%; margin-bottom: 0cm; orphans: 2; widows: 2;">
<span style="color: black;"> <span style="font-family: FreeSans, sans-serif;"><span style="font-size: x-large;"><b>6º
ANO A – PEDRO HENRIQUE </b></span></span></span>
</p>
<p style="font-style: normal; font-variant: normal; letter-spacing: normal; line-height: 100%; margin-bottom: 0cm; orphans: 2; widows: 2;">
<span style="color: #18a303;"> <span style="font-family: FreeSans, sans-serif;"><span style="font-size: x-large;"><b>6º
ANO B – DAVI OLIVEIRA</b></span></span></span></p>
<p style="font-style: normal; font-variant: normal; letter-spacing: normal; line-height: 100%; margin-bottom: 0cm; orphans: 2; widows: 2;">
<span style="color: black;"> <span style="font-family: FreeSans, sans-serif;"><span style="font-size: x-large;"><b>7º
ANO A – ALEXIA</b></span></span></span></p>
<p style="font-style: normal; font-variant: normal; letter-spacing: normal; line-height: 100%; margin-bottom: 0cm; orphans: 2; widows: 2;">
<span style="color: #18a303;"> <span style="font-family: FreeSans, sans-serif;"><span style="font-size: x-large;"><b>8º
ANO B – JOANA</b></span></span></span></p>
<p style="font-style: normal; font-variant: normal; letter-spacing: normal; line-height: 100%; margin-bottom: 0cm; orphans: 2; widows: 2;">
<br />
</p>
<p align="center" style="font-style: normal; font-variant: normal; letter-spacing: normal; line-height: 100%; margin-bottom: 0cm; orphans: 2; widows: 2;">
<span style="color: #f10d0c;"><span style="font-family: FreeSans, sans-serif;"><span style="font-size: xx-large;"><u><b>MATEMÁTICA</b></u></span></span></span></p>
<p style="font-style: normal; font-variant: normal; letter-spacing: normal; line-height: 100%; margin-bottom: 0cm; orphans: 2; widows: 2;">
<br />
</p>
<p style="font-style: normal; font-variant: normal; letter-spacing: normal; line-height: 100%; margin-bottom: 0cm; orphans: 2; widows: 2;">
<span style="color: black;"><span style="color: #00a933;"> <span style="font-family: FreeSans, sans-serif;"><span style="font-size: x-large;"><b>6º
ANO A - RAFAEL</b></span><b> </b></span></span></span>
</p>
<p style="font-style: normal; font-variant: normal; letter-spacing: normal; line-height: 100%; margin-bottom: 0cm; orphans: 2; widows: 2;">
<span style="color: black;"> <span style="font-family: FreeSans, sans-serif;"><span style="font-size: x-large;"><b>6º
ANO B – MARIA SOFIA </b></span></span></span>
</p>
<p style="font-style: normal; font-variant: normal; letter-spacing: normal; line-height: 100%; margin-bottom: 0cm; orphans: 2; widows: 2;">
<span style="color: #18a303;"> <span style="font-family: FreeSans, sans-serif;"><span style="font-size: x-large;"><b>7º
ANO A – HEITOR AUDRIN</b></span></span></span></p>
<p style="font-style: normal; font-variant: normal; letter-spacing: normal; line-height: 100%; margin-bottom: 0cm; orphans: 2; widows: 2;">
<span style="color: black;"> <span style="font-family: FreeSans, sans-serif;"><span style="font-size: x-large;"><b>7º
ANO B – LUY HENRIQUE</b></span></span></span></p>
<p style="font-style: normal; font-variant: normal; letter-spacing: normal; line-height: 100%; margin-bottom: 0cm; orphans: 2; widows: 2;">
<span style="color: #18a303;"> <span style="font-family: FreeSans, sans-serif;"><span style="font-size: x-large;"><b>8º
ANO A – SARA PENA</b></span></span></span></p>
<p style="font-style: normal; font-variant: normal; letter-spacing: normal; line-height: 100%; margin-bottom: 0cm; orphans: 2; widows: 2;">
<span style="color: black;"> <span style="font-family: FreeSans, sans-serif;"><span style="font-size: x-large;"><b>8º
ANO B – KAREN </b></span></span></span>
</p>
<p style="font-style: normal; font-variant: normal; letter-spacing: normal; line-height: 100%; margin-bottom: 0cm; orphans: 2; widows: 2;">
<span style="color: #18a303;"> <span style="font-family: FreeSans, sans-serif;"><span style="font-size: x-large;"><b>1º
ANO MAT 1 – MARIA VICTÓRIA</b></span></span></span></p>
<p style="line-height: 100%; margin-bottom: 0cm; orphans: 2; widows: 2;">
<span style="font-variant: normal;"><span style="color: black;"><span style="letter-spacing: normal;">
<span style="font-family: FreeSans, sans-serif;"><span style="font-size: x-large;"><span style="font-style: normal;"><b>2º
ANO </b></span></span></span></span></span></span><span style="color: black;"><span style="font-variant: normal;"><span style="color: black;"><span style="font-size: x-large;"><span style="letter-spacing: normal;"><span style="font-style: normal;"><b>MAT
1</b></span></span></span></span></span><span style="font-variant: normal;"><span style="color: black;"><span style="font-size: x-large;"><span style="letter-spacing: normal;"><span style="font-style: normal;"><b>
– </b></span></span></span></span></span><span style="font-variant: normal;"><span style="color: black;"><span style="font-size: x-large;"><span style="letter-spacing: normal;"><span style="font-style: normal;"><b>RAQUEL
</b></span></span></span></span></span></span>
</p>
<p style="font-style: normal; font-variant: normal; letter-spacing: normal; line-height: 100%; margin-bottom: 0cm; orphans: 2; widows: 2;">
<span style="color: #00a933;"> <span style="font-family: FreeSans, sans-serif;"><span style="font-size: x-large;"><b>2º
ANO MAT 2 – NATÁLIA</b></span></span></span></p>
<p style="font-style: normal; font-variant: normal; letter-spacing: normal; line-height: 100%; margin-bottom: 0cm; orphans: 2; widows: 2;">
<span style="color: black;"> <span style="font-family: FreeSans, sans-serif;"><span style="font-size: x-large;"><b>3º
ANO MAT 1 – MATHEUS</b></span></span></span></p>
<p style="font-style: normal; font-variant: normal; letter-spacing: normal; line-height: 100%; margin-bottom: 0cm; orphans: 2; widows: 2;">
<span style="color: #18a303;"> <span style="font-family: FreeSans, sans-serif;"><span style="font-size: x-large;"><b>3º
ANO MAT 2 – TAYNÁ</b></span></span></span>
</p>
<p><style type="text/css">p { margin-bottom: 0.25cm; line-height: 115%; background: transparent }</style></p>Unknownnoreply@blogger.comtag:blogger.com,1999:blog-6114836858765981739.post-70881373162763046682022-04-20T12:43:00.002-07:002022-04-20T12:43:31.690-07:00DIVISÃO COM RACIONAIS<p> </p><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLxxxCZEiHmpywvUC4Fgbfs9YrZC49T-BygRGt8qZc9pT5-xktVa90FvyP6WFurGS-hGvQ-mb_XPwBotDCUPc1ICS_DPiz8rsyhU-0Nd4_v-o2fMjxwCfcLWb6NPaON0LPEFWuUnSuurwIZwSZioqP_r-HgtBrN6vCocThMMLXWd8l8oafGqPWAZbm/s768/MDIVI.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="352" data-original-width="768" height="259" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLxxxCZEiHmpywvUC4Fgbfs9YrZC49T-BygRGt8qZc9pT5-xktVa90FvyP6WFurGS-hGvQ-mb_XPwBotDCUPc1ICS_DPiz8rsyhU-0Nd4_v-o2fMjxwCfcLWb6NPaON0LPEFWuUnSuurwIZwSZioqP_r-HgtBrN6vCocThMMLXWd8l8oafGqPWAZbm/w563-h259/MDIVI.jpg" width="563" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><br /> </div><br /><p></p>Unknownnoreply@blogger.comtag:blogger.com,1999:blog-6114836858765981739.post-63738231667845279642022-04-20T12:39:00.001-07:002022-04-20T12:39:47.377-07:00MULTIPLICAÇÃO COM RACIONAIS<p> </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEg5LYuERBuGKCkWQgGKKG_bP-P2RNq6UPD1YWaurggzJJ3VmyOLXmpG6xpCeWopVi13gTHx7pndyiMxLrPirqZ5HZkSPnhe9dB7pBpxLAflrrc-NYkWa8WcyVOkd5knFs1IJNi5ZSsc56hP9RoijdkEi80nl3GS01SjthINDhXcihR8wC2RqnF63Z4y" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="" data-original-height="381" data-original-width="689" height="334" src="https://blogger.googleusercontent.com/img/a/AVvXsEg5LYuERBuGKCkWQgGKKG_bP-P2RNq6UPD1YWaurggzJJ3VmyOLXmpG6xpCeWopVi13gTHx7pndyiMxLrPirqZ5HZkSPnhe9dB7pBpxLAflrrc-NYkWa8WcyVOkd5knFs1IJNi5ZSsc56hP9RoijdkEi80nl3GS01SjthINDhXcihR8wC2RqnF63Z4y=w537-h334" width="537" /></a></div><br /><p></p>Unknownnoreply@blogger.comtag:blogger.com,1999:blog-6114836858765981739.post-27374488516826414302021-06-10T05:11:00.002-07:002021-06-10T05:11:53.532-07:00ALUNO DESTAQUES 2021 COLÉGIO SANDRA MARIA - PE<b><span style="background-color: #fcff01; font-family: georgia;">GEOMETRIA </span></b><div><br /></div><div><b><span style="font-family: arial;">6º ANO A – ALEXIA CRYS</span></b></div><div><b><span style="font-family: arial;">6º ANO B – CAUÃ DURVAL</span></b></div><div><b><span style="font-family: arial;">7º ANO A – CARLOS HENRIQUE </span></b></div><div><b><span style="font-family: arial;">7º ANO B - CAIO </span></b></div><div><b><span style="font-family: arial;">8º ANO B – THICIANY DA SILVA </span></b></div><div><span style="background-color: #fcff01;"><br /></span></div><div><b style="background-color: #fcff01;">MATEMÁTICA </b></div><div><b><br /></b></div><div><b><span style="font-family: arial;">6º ANO B – LUY HENRIQUE - BEATRIZ - ELLEN SILVA- KAUAN – JOÃO ANTONIO </span></b></div><div><b><span style="font-family: arial;">7º ANO A – CARLOS HENRIQUE </span></b></div><div><b><span style="font-family: arial;">7º ANO B – SARAH PENA </span></b></div><div><b><span style="font-family: arial;">8º ANO A – CAIO – JOÃO GUILHERME – YORRAN </span></b></div><div><b><span style="font-family: arial;">8º ANO B – WANDERSON </span></b></div><div><b><span style="font-family: arial;">1º ANO – ALLANA – ANA ALICE – JOSÉ TEMUDO – MARIA BEATRIZ – RAQUEL TEÓFILO </span></b></div><div><b><span style="font-family: arial;">2º ANO – CATARINA – NICHOLAS – RAFAEL - TAYNÁ – VICTOR SÁ </span></b></div><div><b><span style="font-family: arial;">3º ANO – EWERTON </span></b></div><div><br /></div><div> <span style="font-family: verdana; font-size: x-large;"><b style="background-color: #fcff01;">VOCÊS SÃO 10 </b></span></div>Unknownnoreply@blogger.comtag:blogger.com,1999:blog-6114836858765981739.post-90841369633957611282021-05-20T17:17:00.015-07:002021-06-10T05:41:55.484-07:00NÚMEROS COMPLEXOS<b><u style="background-color: #fcff01;">NÚMEROS COMPLEXOS</u></b><div><b><u><br /></u></b></div><div><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;">Denominamos número complexo ao número </p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><b><br /></b></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><b>Z </b>da forma <b>Z = </b><span style="color: #c9211e;"><b>a </b></span><b>+ </b><span style="color: #c9211e;"><b>bi</b></span>, sendo<b> a </b>e <b>b </b>números reais.</p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><br /></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;">Onde:</p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><b><br /></b></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><b>Z</b> é o número complexo</p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><b><br /></b></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><b>a </b>é a parte real de Z</p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><b><br /></b></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><b>bi </b>é a parte imaginária de Z</p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><b><br /></b></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><b>i </b>é a unidade imaginária.</p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><br /></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;">A unidade imaginária i é definida segundo a igualdade</p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><br /></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"> <span style="font-size: 15pt;"><b>i</b></span><sup><span style="font-size: x-small;"><b>2 </b></span></sup><span style="font-size: 15pt;"><b>= -1, </b></span><span style="font-size: 15pt;">onde podemos escrever : </span><b><span style="font-size: 20px;">i =</span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVTg8nbfV3lclXZsi0AdNcv64aKLCNx7J1L98pr3u4nUH0PDi8zdAROojAo2xLm-OSKsGqCQC9KOjUjadUFp4NtfdmX2BGKpUSRh-tcNDZf__vSg4Z5nGS7f1OkV4VGkOh1I3fE75z0Js/" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img alt="" data-original-height="183" data-original-width="275" height="23" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVTg8nbfV3lclXZsi0AdNcv64aKLCNx7J1L98pr3u4nUH0PDi8zdAROojAo2xLm-OSKsGqCQC9KOjUjadUFp4NtfdmX2BGKpUSRh-tcNDZf__vSg4Z5nGS7f1OkV4VGkOh1I3fE75z0Js/w35-h23/image.png" width="35" /></a></b></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><br /></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><br /></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;">Com a utilização desse novo símbolo podemos determinar as raízes</p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"> </p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;">de uma equação do 2<sup>o</sup> grau que tem delta negativo. <b>( </b><span style="font-family: Liberation Serif, serif;"><b>Δ < 0 ).</b></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><br /></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="font-family: Liberation Serif, serif;"><u><b><span style="background: rgb(255, 255, 0);">Exemplo:</span></b></u></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><br /></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="font-family: Liberation Serif, serif;"><b>Determine as raízes da equação: </b></span><span style="font-family: Liberation Serif, serif;"><span style="font-size: 15pt;"><b>x</b></span></span><sup><span style="font-family: Liberation Serif, serif;"><span style="font-size: 15pt;"><b>2</b></span></span></sup><span style="font-family: Liberation Serif, serif;"><span style="font-size: 15pt;"><b> – 2x + 2 = 0</b></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><br /></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><br /></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: #c9211e;"><b>Resposta </b></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><b style="color: #c9211e;"><br /></b></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><b style="color: #c9211e;">temos: a = 1 , b = - 2 e c = 2</b></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><br /></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: #c9211e;"><b><span style="background: rgb(255, 255, 255);"><span style="color: black;"><span style="font-family: Liberation Serif, serif;">Δ = b</span></span><span style="color: black;"><sup><span style="font-family: Liberation Serif, serif;">2</span></sup></span><span style="color: black;"><span style="font-family: Liberation Serif, serif;"> – 4 . a . c</span></span><span style="font-family: Liberation Serif, serif;"></span></span></b></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><br /></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: #c9211e;"><b><span style="font-family: Liberation Serif, serif;">Δ = ( -2 )</span><sup><span style="font-family: Liberation Serif, serif;">2</span></sup><span style="font-family: Liberation Serif, serif;"> – 4 . 1 . 2</span></b></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: #c9211e;"><span style="font-family: Liberation Serif, serif;"><b><br /></b></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: #c9211e;"><span style="font-family: Liberation Serif, serif;"><b>Δ = 4 – 8</b></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: #c9211e;"><b><span style="background: rgb(255, 255, 255);"><span style="font-family: Liberation Serif, serif;"><span style="background: rgb(255, 255, 0);"><br /></span></span></span></b></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: #c9211e;"><b><span style="background: rgb(255, 255, 255);"><span style="font-family: Liberation Serif, serif;"><span style="background: rgb(255, 255, 0);">Δ = - 4 </span></span><span style="font-family: Liberation Serif, serif;">impossível no conjunto dos reais.</span></span></b></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="background: rgb(255, 255, 255);"><span style="font-family: Liberation Serif, serif;"></span></span></p><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; color: #c9211e; font-weight: bold; text-align: left;"><span style="font-family: Liberation Serif, serif;"><br /><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhevyCAYIlNvgsZZnHwMe-wfOrFrNiaWFl8pwAWLw0X8n40oFZqi6Kk2PMA_n2BbfKj0iI90d6hWTaAFbXzXT1Gc7_w_TTenXk8DPm6Yhlu1uqblqgkj4UGKmVMaSSQlM3nn8MJFJXDjMc/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="305" data-original-width="1141" height="136" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhevyCAYIlNvgsZZnHwMe-wfOrFrNiaWFl8pwAWLw0X8n40oFZqi6Kk2PMA_n2BbfKj0iI90d6hWTaAFbXzXT1Gc7_w_TTenXk8DPm6Yhlu1uqblqgkj4UGKmVMaSSQlM3nn8MJFJXDjMc/w493-h136/image.png" width="493" /></a></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div></span></div></div><p></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: black;"><span style="font-family: Liberation Serif, serif;"><u><b><span style="background: rgb(255, 255, 0);">Exercícios</span></b></u></span></span></p><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; color: #c9211e; text-align: left;"><div class="separator" style="clear: both; font-weight: bold;"><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-weight: 400; line-height: 1px; margin-bottom: 0cm;"><br /></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-weight: 400; line-height: 1px; margin-bottom: 0cm;"><span style="color: black;"><span style="font-family: Liberation Serif, serif;"><b><span style="background: rgb(255, 255, 255);">1.) Calcule as raízes nas equações:</span></b></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-weight: 400; line-height: 1px; margin-bottom: 0cm;"><br /></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-weight: 400; line-height: 1px; margin-bottom: 0cm;"><span face="Liberation Sans Narrow, sans-serif"><span style="font-size: 12pt;"><span style="color: black;"><b><span style="background: rgb(255, 255, 255);">a) </span></b></span><span style="color: black;"><b><span style="background: rgb(255, 255, 255);">x</span></b></span><span style="color: black;"><sup><b><span style="background: rgb(255, 255, 255);">2 </span></b></sup></span><span style="color: black;"><b><span style="background: rgb(255, 255, 255);">+2x + 5 = 0</span></b></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-weight: 400; line-height: 1px; margin-bottom: 0cm;"><br /></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-weight: 400; line-height: 1px; margin-bottom: 0cm;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="Liberation Sans Narrow, sans-serif"><span style="font-size: 12pt;"><b><span style="background: rgb(255, 255, 255);">b</span></b></span></span></span></span><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="Liberation Sans Narrow, sans-serif"><span style="font-size: 12pt;"><b><span style="background: rgb(255, 255, 255);">) </span></b></span></span></span></span><em><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: #212529;"><span face="Liberation Sans Narrow, sans-serif"><span style="font-size: 12pt;"><b><span style="background: rgb(255, 255, 255);">−</span></b></span></span></span></span></em><em><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: #212529;"><span face="Liberation Sans Narrow, sans-serif"><span style="font-size: 12pt;"><span style="font-style: normal;"><b><span style="background: rgb(255, 255, 255);">x² + 4x − 29 = 0</span></b></span></span></span></span></span></em><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: #212529;"><span face="Liberation Sans Narrow, sans-serif"><span style="font-size: 12pt;"><b><span style="background: rgb(255, 255, 255);">.</span></b></span></span></span></span></p></div><div class="separator" style="clear: both; font-weight: bold; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 400; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="color: #212529;"><span face="Liberation Sans Narrow, sans-serif"><span style="font-size: 12pt;"><u><b><span style="background: rgb(255, 255, 0);">CARACTERÍSTICAS DE UM NÚMERO COMPLEXO</span></b></u></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 400; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span style="font-family: Raleway;"><span style="font-size: 12pt;"><span style="background: rgb(255, 255, 255);"><br /></span></span></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 400; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span style="font-family: Raleway;"><span style="font-size: 12pt;"><u><b><span style="background: rgb(255, 255, 255);"><br class="Apple-interchange-newline" />I</span></b></u></span></span></span></span><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span style="font-family: Raleway;"><span style="font-size: 12pt;"><u><b><span style="background: rgb(255, 255, 255);">MAGINÁRIO PURO: </span></b></u></span></span></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 400; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span style="font-family: Raleway;"><span style="font-size: 12pt;"><u><b><span style="background: rgb(255, 255, 255);"><br /></span></b></u></span></span></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 400; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span style="font-family: Raleway;"><span style="font-size: 12pt;"><span style="background: rgb(255, 255, 255);"><br /></span></span></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 400; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span style="font-family: Raleway;"><span style="font-size: 12pt;"><span style="background: rgb(255, 255, 255);">Quando a </span></span></span></span></span><span style="border: none; display: inline-block; padding: 0cm;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span style="font-family: inherit;"><span style="font-size: 12pt;"><span style="background: rgb(255, 255, 255);"><strong>parte real é nula</strong></span></span></span></span></span></span><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span style="font-family: Raleway;"><span style="font-size: 12pt;"><span style="background: rgb(255, 255, 255);">, por exemplo, –5</span></span></span></span></span><span style="border: none; display: inline-block; padding: 0cm;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span style="font-family: inherit;"><span style="font-size: 12pt;"><span style="background: rgb(255, 255, 255);"><em>i </em></span></span></span></span></span></span><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span style="font-family: Raleway;"><span style="font-size: 12pt;"><span style="background: rgb(255, 255, 255);">e 5</span></span></span></span></span><span style="border: none; display: inline-block; padding: 0cm;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span style="font-family: inherit;"><span style="font-size: 12pt;"><span style="background: rgb(255, 255, 255);"><em>i</em></span></span></span></span></span></span><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span style="font-family: Raleway;"><span style="font-size: 12pt;"><span style="background: rgb(255, 255, 255);"> </span></span></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 400; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span style="font-family: Raleway;"><span style="font-size: 12pt;"><span style="background: rgb(255, 255, 255);"><br /></span></span></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 400; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span style="font-family: Raleway;"><span style="font-size: 12pt;"><span style="background: rgb(255, 255, 255);"> são imaginários puros </span></span></span></span></span><span style="background-color: white; font-family: Raleway; font-size: 12pt;"> por não possuírem parte real.</span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: 400; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="background-color: white; font-family: Raleway; font-size: 12pt;"><br /></span></p><p style="background: rgb(255, 255, 255); border: none; color: black; font-weight: 400; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><strong><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;"><u><b><br /></b></u></span></span></span></span></strong></p><p style="background: rgb(255, 255, 255); border: none; color: black; font-weight: 400; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><strong><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;"><u><b>Exemplo:</b></u></span></span></span></span></strong><strong><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;"><b> </b></span></span></span></span></strong><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;">Determine o valor de </span></span></span></span><strong><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;"><b>k </b></span></span></span></span></strong><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;">para que o número complexo</span></span></span></span></p><p style="background: rgb(255, 255, 255); border: none; color: black; font-weight: 400; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><strong><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;"><b><br /></b></span></span></span></span></strong></p><p style="background: rgb(255, 255, 255); border: none; color: black; font-weight: 400; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><strong><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;"><b><br /></b></span></span></span></span></strong></p><p style="background: rgb(255, 255, 255); border: none; color: black; font-weight: 400; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;"></span></span></span></span><strong><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;"><b>z = (k – </b></span></span></span></span></strong><strong><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;"><b>8</b></span></span></span></span></strong><strong><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;"><b>) + 3i </b></span></span></span></span></strong><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;">seja </span></span></span></span><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;">i</span></span></span></span><span face="Helvetica, Arial, sans-serif" style="font-size: 12pt;">maginário puro: </span></p><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-weight: 400; line-height: 1.15px; margin-bottom: 0.25cm;"><em><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: #c9211e;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;"><span style="font-style: normal;"><b><br /></b></span></span></span></span></span></em></p><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-weight: 400; line-height: 1.15px; margin-bottom: 0.25cm;"><em><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: #c9211e;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;"><span style="font-style: normal;"><b><br /></b></span></span></span></span></span></em></p><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-weight: 400; line-height: 1.15px; margin-bottom: 0.25cm;"><em><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: #c9211e;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;"><span style="font-style: normal;"><b>Resolução</b></span></span></span></span></span></em></p><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: #c9211e;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;"><b><br /></b></span></span></span></span></p><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: #c9211e;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;"><b><br /></b><br /></span></span></span></span></p><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: #c9211e;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;">Para que o </span></span></span></span><span face="Helvetica, Arial, sans-serif" style="color: #c9211e; font-size: 12pt; text-align: left;">número seja imaginário puro, a parte</span></p><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; line-height: 1.15px; margin-bottom: 0.25cm;"><span face="Helvetica, Arial, sans-serif" style="color: #c9211e; font-size: 12pt; text-align: left;"><br /></span></p><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; line-height: 1.15px; margin-bottom: 0.25cm;"><span face="Helvetica, Arial, sans-serif" style="color: #c9211e; font-size: 12pt; text-align: left;">real deve ser nula:</span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-weight: 400; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="color: #c9211e;"><br /></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-weight: 400; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="color: #c9211e;"><br /></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-weight: 400; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="color: #c9211e;"> <span style="color: #00a933;"><b>K – 8 = 0 K= 0 + 8 </b></span><span style="color: #00a933;"><b><span style="background: rgb(255, 255, 0);">K = 8</span></b></span></span></p><p style="background: rgb(255, 255, 255); border: none; color: black; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span style="color: black;"><span style="font-family: Raleway;"><span style="font-size: 12pt;"><u><b><br /></b></u></span></span></span></p><p style="background: rgb(255, 255, 255); border: none; color: black; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span style="color: black;"><span style="font-family: Raleway;"><span style="font-size: 12pt;"><u><b><br /></b></u></span></span></span></p><p style="background: rgb(255, 255, 255); border: none; color: black; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span style="color: black;"><span style="font-family: Raleway;"><span style="font-size: 12pt;"><u><b>REAL:</b></u> Quando a parte imaginária é nula, por exemplo, 4 ou 4 + 0i.</span></span></span></p><p style="background: rgb(255, 255, 255); border: none; color: black; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: normal; line-height: 1.15px; margin-bottom: 0.4cm; padding: 0cm;"><span style="color: black;"><span style="font-family: Raleway;"><span style="font-size: 12pt;"><br /></span></span></span></p><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-weight: 400; line-height: 1.15px; margin-bottom: 0.25cm;"><strong><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;"><u><b><br /></b></u></span></span></span></span></strong></p><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-weight: 400; line-height: 1.15px; margin-bottom: 0.25cm;"><strong><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;"><u><b>Exemplo: </b></u></span></span></span></span></strong><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;">Determine o valor de </span></span></span></span><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;"><b>m</b></span></span></span></span><strong><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;"><b> </b></span></span></span></span></strong><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;">para que o número complexo</span></span></span></span></p><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-weight: 400; line-height: 1.15px; margin-bottom: 0.25cm;"><strong><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;"><b><br /></b></span></span></span></span></strong></p><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-weight: 400; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;"></span></span></span></span><strong><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;"><b>z = 3+(</b></span></span></span></span></strong><strong><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;"><b>m</b></span></span></span></span></strong><strong><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;"><b> </b></span></span></span></span></strong><strong><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;">+</span></span></span></span></strong><strong><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;"><b> 4)i </b></span></span></span></span></strong><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;">seja um </span></span></span></span><span style="font-variant-east-asian: normal; font-variant-numeric: normal; text-align: left;"><span style="color: black;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;">número re</span></span></span></span><span face="Helvetica, Arial, sans-serif" style="font-size: 12pt; text-align: left;">al:</span></p><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-weight: 400; line-height: 1.15px; margin-bottom: 0.25cm;"><em><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: #c9211e;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;"><span style="font-style: normal;"><b><br /></b></span></span></span></span></span></em></p><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-weight: 400; line-height: 1.15px; margin-bottom: 0.25cm;"><em><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: #c9211e;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;"><span style="font-style: normal;"><b><br /></b></span></span></span></span></span></em></p><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-weight: 400; line-height: 1.15px; margin-bottom: 0.25cm;"><em><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: #c9211e;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;"><span style="font-style: normal;"><b>Resolução</b></span></span></span></span></span></em></p><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: #c9211e;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;"><b><br /></b><br /></span></span></span></span></p><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: #c9211e;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;"><br /></span></span></span></span></p><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: #c9211e;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;">Para que o número seja real, a parte imaginária deve ser nula:</span></span></span></span></p><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: normal; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="color: #c9211e;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;"><br /></span></span></span></p><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: normal; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="color: #c9211e;"><span face="Helvetica, Arial, sans-serif"><span style="font-size: 12pt;"> <span style="color: #00a933;"><b>m +4 = 0 </b></span><span style="color: #00a933;"><b>m = 0 – 4 </b></span><span style="color: #00a933;"><b><span style="background: rgb(255, 255, 0);">m = - 4</span></b></span></span></span></span></p></div><h2 align="left" class="western" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; break-after: avoid; color: black; font-family: "Liberation Serif", serif; font-size: 18pt; margin-bottom: 0.21cm; margin-top: 0.35cm;"><strong><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 18pt;"><u><b><span style="background: rgb(255, 255, 0);"><br /></span></b></u></span></span></span></span></strong></h2><h2 align="left" class="western" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; break-after: avoid; color: black; font-family: "Liberation Serif", serif; font-size: 18pt; margin-bottom: 0.21cm; margin-top: 0.35cm;"><strong><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 18pt;"><u><b><span style="background: rgb(255, 255, 0);">Adiçã</span></b></u></span></span></span></span></strong><strong><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 18pt;"><u><b><span style="background: rgb(255, 255, 0);">o</span></b></u></span></span></span></span></strong></h2><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;">Considerando-se os complexos:</span></span></span></p><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><br /></b></span></span></span></p><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b>z</b></span><sub><span style="font-size: 12pt;"><b>1</b></span></sub><span style="font-size: 12pt;"><b> = a+bi </b></span><span style="font-size: 12pt;">e </span><span style="font-size: 12pt;"><b>z</b></span><sub><span style="font-size: 12pt;"><b> 2 </b></span></sub><span style="font-size: 12pt;"><b>= c+</b></span><span style="font-size: 12pt;"><b>di </b></span></span></span></p><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><br /></span></span></span></p><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;">a soma<b> </b><b>z</b><sub><b>1</b></sub><b> + z</b><sub><b> 2 </b></sub><sub><b></b></sub>obtida somando-se suas partes reais</span></span></span></p><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><br /></span></span></span></p><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;">e imaginárias separadamente:</span></span></span></p><div class="separator" style="clear: both; color: #c9211e; text-align: left;"><br /></div><br /><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; line-height: 1.15px; margin-bottom: 0.25cm;"><strong style="text-align: left;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;">Exemplos:</span></span></span></span></strong></p><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; line-height: 1.15px; margin-bottom: 0.25cm;"><strong style="text-align: left;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><br /></b></span></span></span></span></strong></p><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; line-height: 1.15px; margin-bottom: 0.25cm;"><strong style="text-align: left;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b>(2 + 3i) + (5 + 4i) = (2+5) + (3 + 4)i = 7 + 7i</b></span></span></span></span></strong></p><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; line-height: 1.15px; margin-bottom: 0.25cm;"><strong style="text-align: left;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><br /></b></span></span></span></span></strong></p><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; line-height: 1.15px; margin-bottom: 0.25cm;"><strong style="text-align: left;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b>2i + (6 + 9i) = (0 + 6) + (2 + 9)i = 6 + 11i</b></span></span></span></span></strong></p><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; line-height: 1.15px; margin-bottom: 0.25cm;"><strong style="text-align: left;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><br /></b></span></span></span></span></strong></p><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; line-height: 1.15px; margin-bottom: 0.25cm;"><strong style="text-align: left;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><br /></b></span></span></span></span></strong></p><p align="justify" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; line-height: 1.15px; margin-bottom: 0.25cm;"><strong style="text-align: left;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b>(5 + 3i) + 3 = (5 + 3) + (3 + 0)i = 8 + 3i</b></span></span></span></span></strong></p><h2 align="justify" class="western" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; break-after: avoid; color: black; font-family: "Liberation Serif", serif; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 0.53cm; margin-bottom: 0.21cm; margin-top: 0.35cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><b><span style="background: rgb(255, 255, 0);"><br /></span></b></span></span></h2><h2 align="justify" class="western" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; break-after: avoid; color: black; font-family: "Liberation Serif", serif; font-size: 18pt; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 0.53cm; margin-bottom: 0.21cm; margin-top: 0.35cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><b><span style="background: rgb(255, 255, 0);">Subtração</span></b></span></span></h2><p align="left" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><br /></span></span></span></p><p align="left" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;">Dados os complexos </span></span></span><b style="font-family: HELVETICA, sans-serif; font-size: 12pt;">z</b><sub style="font-family: HELVETICA, sans-serif;"><b>1</b></sub><b style="font-family: HELVETICA, sans-serif; font-size: 12pt;"> = a - bi </b><span face="HELVETICA, sans-serif" style="font-size: 12pt;">e</span><b style="font-family: HELVETICA, sans-serif; font-size: 12pt;"> z</b><sub style="font-family: HELVETICA, sans-serif;"><b> 2 </b></sub><b style="font-family: HELVETICA, sans-serif; font-size: 12pt;">= c - di </b></p><p align="left" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><br /></b><br /></span></span></span></p><p align="left" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;">a diferença <b></b><b>z</b><sub><b>1</b></sub><b> - z</b><sub><b> 2 </b></sub><sub><b></b></sub>é obtida subtraindo-se suas partes reais</span></span></span></p><p align="left" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><br /></span></span></span></p><p align="left" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;">e imaginárias separadamente:</span></span></span></p><br /><br /><p align="left" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; line-height: 1.15px; margin-bottom: 0.25cm;"><strong><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;">Exemplos</span></span></span></span></strong></p><p align="left" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; line-height: 1.15px; margin-bottom: 0.25cm;"><strong><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><br /></b></span></span></span></span></strong></p><p align="left" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; line-height: 1.15px; margin-bottom: 0.25cm;"><strong><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b>(2 + 3i) - (5 + 4i) = (2 - 5) + (3 - 4)i = -3 - i</b></span></span></span></span></strong></p><p align="left" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; line-height: 1.15px; margin-bottom: 0.25cm;"><strong><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><br /></b></span></span></span></span></strong></p><p align="left" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; line-height: 1.15px; margin-bottom: 0.25cm;"><strong><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b>2i - (6 - 9i) = (0 - 6) + (2 -(-9))i = -6 + 11i</b></span></span></span></span></strong></p><p align="left" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; line-height: 1.15px; margin-bottom: 0.25cm;"><strong><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><br /></b></span></span></span></span></strong></p><p align="left" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: black; line-height: 1.15px; margin-bottom: 0.25cm;"><strong><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b>(5 + 3i) - 3 = (5 - 3) + (3 - 0)i = 2 + 3i</b></span></span></span></span></strong></p></div><div style="margin-left: 1em; margin-right: 1em; text-align: left;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg09yLFdVhA3OBc77TASyFB-I8ydNiPtbY5yXnD3_7JMN9UxjeKcV7rhykTltUdBhA7e8RfSr_UN0oYRmlEkuLxeKfsAk4Tb3fHZCCN3UhpdXRiFnwyB9KHdz_omZ8q363_QDtFm5DpkBI/" style="font-weight: 700; margin-left: 1em; margin-right: 1em;"><br /></a></div></div><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="color: #00a933;"><span face="HELVETICA, sans-serif"><span style="font-size: 18pt;"><b><br /></b></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1.15px; margin-bottom: 0.25cm;"><span face="HELVETICA, sans-serif"><span style="background-color: white; font-size: 24px;"><b>Potenciação:</b></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1.15px; margin-bottom: 0.25cm;"><span face="HELVETICA, sans-serif"><span style="background-color: white; font-size: 24px;"><b><br /></b></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1.15px; margin-bottom: 0.25cm;"><span face="HELVETICA, sans-serif"><span style="background-color: white; font-size: 24px;"><b><br /></b></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1.15px; margin-bottom: 0.25cm;"><span face="HELVETICA, sans-serif"><span style="background-color: white; font-size: 24px;"><b> Na potenciação de números complexos encontramos </b></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1.15px; margin-bottom: 0.25cm;"><span face="HELVETICA, sans-serif"><span style="background-color: white; font-size: 24px;"><b><br /></b></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1.15px; margin-bottom: 0.25cm;"><span face="HELVETICA, sans-serif"><span style="background-color: white; font-size: 24px;"><b>uma regularidade, os resultados começam a se repetir</b></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1.15px; margin-bottom: 0.25cm;"><span face="HELVETICA, sans-serif"><span style="background-color: white; font-size: 24px;"><b><br /></b></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1.15px; margin-bottom: 0.25cm;"><span face="HELVETICA, sans-serif"><span style="background-color: white; font-size: 24px;"><b>à partir do 4 termo. </b></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1.15px; margin-bottom: 0.25cm;"><span face="HELVETICA, sans-serif"><span style="background-color: white; font-size: 24px;"><b><br /></b></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1.15px; margin-bottom: 0.25cm;"><span face="HELVETICA, sans-serif"><span style="background-color: white; font-size: 24px;"><b>veja: </b></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1.15px; margin-bottom: 0.25cm;"><span face="HELVETICA, sans-serif"><span style="background-color: white; font-size: 24px;"><b><br /></b></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1.15px; margin-bottom: 0.25cm;"><span face="HELVETICA, sans-serif"><span style="background-color: white; font-size: 24px;"><b></b></span></span></p><div class="separator" style="clear: both; text-align: left;"><span face="HELVETICA, sans-serif"><b><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhrlB5R0aaKCoyrn1lY23ZgAHYY9qU2YdXEIR_PsmsBniqjKCif8fGNVJjGYraKoh03khxscLUE50xadFkuC4DE_iQUsnxqST0SJzUJuyObvTdS_3LQsd9RzbIj0czioyDVZnOQuFPN0yc/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="247" data-original-width="175" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhrlB5R0aaKCoyrn1lY23ZgAHYY9qU2YdXEIR_PsmsBniqjKCif8fGNVJjGYraKoh03khxscLUE50xadFkuC4DE_iQUsnxqST0SJzUJuyObvTdS_3LQsd9RzbIj0czioyDVZnOQuFPN0yc/" width="170" /></a></b></span></div><div class="separator" style="clear: both; text-align: left;"><span face="HELVETICA, sans-serif"><b> Para resolver uma potencia temos que dividir o expoente por 4 e considerar o resto</b></span></div><div class="separator" style="clear: both; text-align: left;"><span face="HELVETICA, sans-serif"><b><br /></b></span></div><div class="separator" style="clear: both; text-align: left;"><span face="HELVETICA, sans-serif"><b>como novo expoente. </b></span></div><div class="separator" style="clear: both; text-align: left;"><span face="HELVETICA, sans-serif"><b><br /></b></span></div><div class="separator" style="clear: both; text-align: left;"><span face="HELVETICA, sans-serif"><b>veja:</b></span></div><div class="separator" style="clear: both; text-align: left;"><span face="HELVETICA, sans-serif"><b><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVxBrH-p0p2OYbBT55MO34rjz4MysPcQyIFZlFcHt_M_Zopub9-iJL9ooPnaUM18xBALVITZGh-FVjCbBv9mJxwcANDesL3bn6vVAmZrvbK9ka2nEKYxVkl3__Uj-L6D4EwfVb-YyqxQE/" style="margin-left: 1em; margin-right: 1em;"></a><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVxBrH-p0p2OYbBT55MO34rjz4MysPcQyIFZlFcHt_M_Zopub9-iJL9ooPnaUM18xBALVITZGh-FVjCbBv9mJxwcANDesL3bn6vVAmZrvbK9ka2nEKYxVkl3__Uj-L6D4EwfVb-YyqxQE/" style="margin-left: 1em; margin-right: 1em;"></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSNxvxfhNqpmK9QxX-iv74T4uqHd8R_WnT5Kq4_IGQg4BZ-5hucsoMiKqRjPMWlNHFC8U7gUAi2-F6kPUx3N5wgQJDjRHiPlbAIhDQaGKfGgLYunpRswe3iGRRIaxByQc8GxtEtMmQWso/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="137" data-original-width="538" height="81" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSNxvxfhNqpmK9QxX-iv74T4uqHd8R_WnT5Kq4_IGQg4BZ-5hucsoMiKqRjPMWlNHFC8U7gUAi2-F6kPUx3N5wgQJDjRHiPlbAIhDQaGKfGgLYunpRswe3iGRRIaxByQc8GxtEtMmQWso/" width="320" /></a></div><br /></div><div class="separator" style="clear: both; text-align: left;">fazemos da mesmo forma com qualquer potência.</div><br /><br /></b></span></div><p></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="color: #00a933;"><span face="HELVETICA, sans-serif"><span style="font-size: 18pt;"><b>1.) Calcule o valor de cada expressão:</b></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="color: #00a933;"><span face="HELVETICA, sans-serif"><span style="font-size: 18pt;"><b><br /></b></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="font-size: 18pt;"><b><span face="HELVETICA, sans-serif">a) </span><span style="font-family: Liberation Serif, serif;">i</span><sup><span style="font-family: Liberation Serif, serif;">125</span></sup><span style="font-family: Liberation Serif, serif;"> – i</span><sup><span style="font-family: Liberation Serif, serif;">126</span></sup><span style="font-family: Liberation Serif, serif;"> + i</span><sup><span style="font-family: Liberation Serif, serif;">127 </span></sup><span style="font-family: Liberation Serif, serif;">– i</span><sup><span style="font-family: Liberation Serif, serif;">128</span></sup></b></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="font-size: 18pt;"><b><sup><span style="font-family: Liberation Serif, serif;"><br /></span></sup></b></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="color: black;"><span style="font-size: 18pt;"><b>b 2<span style="font-family: Liberation Serif, serif;">i</span><sup><span style="font-family: Liberation Serif, serif;">125</span></sup><span style="font-family: Liberation Serif, serif;"> </span><span style="font-family: Liberation Serif, serif;">+ 3</span><span style="font-family: Liberation Serif, serif;">i</span><sup><span style="font-family: Liberation Serif, serif;">12</span></sup><sup><span style="font-family: Liberation Serif, serif;">0</span></sup><span style="font-family: Liberation Serif, serif;"> - </span><span style="font-family: Liberation Serif, serif;">5</span><span style="font-family: Liberation Serif, serif;">i</span><sup><span style="font-family: Liberation Serif, serif;">2</span></sup><sup><span style="font-family: Liberation Serif, serif;">0</span></sup><sup><span style="font-family: Liberation Serif, serif;">7 </span></sup><span style="font-family: Liberation Serif, serif;">– </span><span style="font-family: Liberation Serif, serif;">2</span><span style="font-family: Liberation Serif, serif;">i</span><sup><span style="font-family: Liberation Serif, serif;">1</span></sup><sup><span style="font-family: Liberation Serif, serif;">0</span></sup><sup><span style="font-family: Liberation Serif, serif;">28</span></sup></b></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="color: black;"><span style="font-size: 18pt;"><b><sup><span style="font-family: Liberation Serif, serif;"><br /></span></sup></b></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="font-size: 18pt;"><b><span style="font-family: Liberation Serif, serif;">c) 3i</span><sup><span style="font-family: Liberation Serif, serif;">1205 </span></sup><span style="font-family: Liberation Serif, serif;">– 4i</span><sup><span style="font-family: Liberation Serif, serif;">216</span></sup><span style="font-family: Liberation Serif, serif;"> - 2i</span><sup><span style="font-family: Liberation Serif, serif;">327 </span></sup><span style="font-family: Liberation Serif, serif;">+ 3i</span><sup><span style="font-family: Liberation Serif, serif;">208</span></sup></b></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="background: rgb(255, 255, 255);"><span style="font-family: Liberation Serif, serif;"><br /></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><br /></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><span style="background: rgb(255, 255, 0);">MULTIPLICAÇÃO DE NÚMEROS COMPLEXOS</span></b></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><br /></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><span style="background: rgb(255, 255, 255);">Ao multiplicar dois números complexos devemos proceder como expressões algébricas, aplicando a <u><span style="background: rgb(255, 233, 148);">propriedade distributiva </span></u>e as potências de i:</span></b></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><br /></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><span style="background: rgb(255, 255, 255);">Exemplo: a) z<sub>1 </sub>= 2 + 3i e z<sub>2 </sub>= 1 – 4i, determine <span style="background: rgb(255, 255, 0);">Z</span><sub><span style="background: rgb(255, 255, 0);">1 </span></sub><span style="background: rgb(255, 255, 0);">. Z</span><sub><span style="background: rgb(255, 255, 0);">2</span></sub></span></b></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><br /></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: red;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><span style="background: rgb(255, 255, 255);">Resposta:</span></b></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: red;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><span style="background: rgb(255, 255, 255);"><br /></span></b></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: red;"><span style="background: rgb(255, 255, 255);"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b>( 2 + 3i) . ( 1 – 4i ) <span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span face="HELVETICA, sans-serif">= 2 . 1 </span></span><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span face="HELVETICA, sans-serif">+</span></span><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span face="HELVETICA, sans-serif"> 2.(-4i) + 3i . 1 + 3i . (-4i ) </span></span></b></span></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: red;"><span style="background: rgb(255, 255, 255);"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span face="HELVETICA, sans-serif"><br /></span></span></b></span></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: red;"><span style="background: rgb(255, 255, 255);"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span face="HELVETICA, sans-serif">= 2 - </span></span><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: #00a933;"><span face="HELVETICA, sans-serif">8i + 3i</span></span></span><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span face="HELVETICA, sans-serif"> -12</span></span><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: purple;"><span face="HELVETICA, sans-serif">i</span></span></span><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: purple;"><sup><span face="HELVETICA, sans-serif">2</span></sup></span></span><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: purple;"><span face="HELVETICA, sans-serif"> </span></span></span></b></span></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: red;"><span style="background: rgb(255, 255, 255);"><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"></span><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span face="HELVETICA, sans-serif"> </span></span></b></span></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: red;"><span style="background: rgb(255, 255, 255);"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span face="HELVETICA, sans-serif"> 2 </span></span><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: #00a933;"><span face="HELVETICA, sans-serif">- 5i </span></span></span><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span face="HELVETICA, sans-serif">-12.( </span></span><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: purple;"><span face="HELVETICA, sans-serif">-1 </span></span></span><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span face="HELVETICA, sans-serif">)</span></span></b></span></span></span></span></p><div><span style="color: red;"><span style="background: rgb(255, 255, 255);"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span face="HELVETICA, sans-serif"><br /></span></span></b></span></span></span></span></div><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><b style="background-color: white; color: red; font-size: 12pt;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span face="HELVETICA, sans-serif"> = </span></span><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: #2a6099;"><span face="HELVETICA, sans-serif">2 </span></span></span><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: #00a933;"><span face="HELVETICA, sans-serif">– 5i </span></span></span><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span face="HELVETICA, sans-serif">+</span></span><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: #2a6099;"><span face="HELVETICA, sans-serif"> 12</span></span></span></b></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: red;"><span style="background: rgb(255, 255, 255);"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: #2a6099;"><span face="HELVETICA, sans-serif"></span></span></span><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span face="HELVETICA, sans-serif"> </span></span></b></span></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: red;"><span style="background: rgb(255, 255, 255);"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span face="HELVETICA, sans-serif"> = </span></span><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: #2a6099;"><span face="HELVETICA, sans-serif">14 - </span></span></span><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span style="color: #00a933;"><span face="HELVETICA, sans-serif">5i</span></span></span><span style="font-variant-east-asian: normal; font-variant-numeric: normal;"><span face="HELVETICA, sans-serif"></span></span></b></span></span></span></span></p><p align="left" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="background-color: #fcff01;"><u><b><br /></b></u></span></p><p align="left" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1.15px; margin-bottom: 0.25cm;"><span style="background-color: #fcff01;"><u><b><br /><br /></b></u></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><span style="background-attachment: initial; background-clip: initial; background-color: #fcff01; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; background: rgb(252, 255, 1);"><u>Exercícios</u></span></b></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><span style="background: rgb(255, 255, 255);"><br /></span></b></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><span style="background: rgb(255, 255, 255);">1.) Calcule:</span></b></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><span style="background: rgb(255, 255, 255);"><br /></span></b></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><span style="background: rgb(255, 255, 255);">a) ( 2 + 5i ) . ( +2i ) =</span></b></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><br /></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><span style="background: rgb(255, 255, 255);">b) ( 6 – 5i ) ( 4+ i ) =</span></b></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><br /></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><span style="background: rgb(255, 255, 255);">2.) Resolva as expressões:</span></b></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><br /></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><span style="background: rgb(255, 255, 255);">a) 2( 3 + 4i ) + 3( 1 + 2i ) =</span></b></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><span style="background: rgb(255, 255, 255);">b) ( 3 – 4i ) . ( 3 + 4i ) + 4( 5 + i) =</span></b></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><span style="background: rgb(255, 255, 255);">c) 3( 1 – i ) + ( 2 + i ) ( 2 – i ) =</span></b></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><br /></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><br /></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><u><b><span style="background: rgb(255, 255, 0);">CONJUGADO DE UM NÚMERO COMPLEXO</span></b></u></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><br /></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><span style="background: rgb(255, 255, 255);">Denominamos conjugado de um número complexo Z = a + bi ao número complexo</span></b></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><span style="background: rgb(255, 255, 255);"></span></b></span></span></span></p><div class="separator" style="clear: both; text-align: left;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivrnnrDUebSPmnYjgE6KMtCTSSLDNFR07Iv970o-ISvqGFAAIR51Vy9fo-7d5QRvSme-GYUN1gqNEACTB3e0BqvTCW72dq57I9y14Uu3dWuRGHlKhfdmPr4G4Qh7pqA598rLor4A-w_bs/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="68" data-original-width="200" height="46" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivrnnrDUebSPmnYjgE6KMtCTSSLDNFR07Iv970o-ISvqGFAAIR51Vy9fo-7d5QRvSme-GYUN1gqNEACTB3e0BqvTCW72dq57I9y14Uu3dWuRGHlKhfdmPr4G4Qh7pqA598rLor4A-w_bs/w135-h46/image.png" width="135" /></a></b></span></span></span></div><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><br /></b></span></span></span><p></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><br /></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><span style="background: rgb(255, 255, 255);">Ex: Dado o complexo Z = 2 + 5i o seu conjugado é o número</span></b></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><br /></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"></p><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOIYol9su5Y1TfofHlg-kCNNWVC57E8YobIHKJhYZ8lON-HfUL5e7Kt1rFYw7iqlYrQzNq1MKr_K8O8N1GlAu-HbbAtOHx9ozAre7RCBB6oD5rTdPI3r3-LpM3YmGN7JGHlX_BbG5KvIw/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="60" data-original-width="193" height="37" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOIYol9su5Y1TfofHlg-kCNNWVC57E8YobIHKJhYZ8lON-HfUL5e7Kt1rFYw7iqlYrQzNq1MKr_K8O8N1GlAu-HbbAtOHx9ozAre7RCBB6oD5rTdPI3r3-LpM3YmGN7JGHlX_BbG5KvIw/w120-h37/image.png" width="120" /></a></div><div class="separator" style="clear: both; text-align: left;"><b style="color: #c9211e; font-family: HELVETICA, sans-serif; font-size: 12pt;"><span style="background: rgb(255, 255, 255);"><br /></span></b></div><div class="separator" style="clear: both; text-align: left;"><b style="color: #c9211e; font-family: HELVETICA, sans-serif; font-size: 12pt;"><span style="background: rgb(255, 255, 255);"><br /></span></b></div><div class="separator" style="clear: both; text-align: left;"><b style="color: #c9211e; font-family: HELVETICA, sans-serif; font-size: 12pt;"><span style="background: rgb(255, 255, 255);">Para obter o conjugado de um número, conservamos a parte real </span></b></div><div class="separator" style="clear: both; text-align: left;"><b style="color: #c9211e; font-family: HELVETICA, sans-serif; font-size: 12pt;"><span style="background: rgb(255, 255, 255);"><br /></span></b></div><div class="separator" style="clear: both; text-align: left;"><b style="color: #c9211e; font-family: HELVETICA, sans-serif; font-size: 12pt;"><span style="background: rgb(255, 255, 255);">e invertemos o sinal</span></b><b style="color: #c9211e; font-family: HELVETICA, sans-serif; font-size: 12pt;"><span style="background: rgb(255, 255, 255);"> da parte imaginária</span></b><b style="color: #c9211e; font-size: 12pt;"><span style="background: rgb(255, 255, 255);">.</span></b></div><div class="separator" style="clear: both; text-align: left;"><b style="color: #c9211e; font-size: 12pt;"><span style="background: rgb(255, 255, 255);"><br /></span></b></div><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><u><b><span style="background: rgb(255, 255, 0);">DIVISÃO DE UM NÚMERO COMPLEXO</span></b></u></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><u><b><span style="background: rgb(255, 255, 0);"><br /></span></b></u></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><u><b><span style="background: rgb(255, 255, 0);"></span></b></u></span></span></span></p><div class="separator" style="clear: both; text-align: left;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><u><b><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh4mqEAPGeI6W9VrY4dLw6D0cyP6MJOW2bW6R7kmrCYoFdcneQhVrDdE2JhZzyC8QMvQqQDFkkSkbwkrbXFRrVwB1k0tTNU9WIqncOFEgjFfRgR-Z3a2TQ2YrhnmopchWIcFl-YtAfDuhg/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="342" data-original-width="414" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh4mqEAPGeI6W9VrY4dLw6D0cyP6MJOW2bW6R7kmrCYoFdcneQhVrDdE2JhZzyC8QMvQqQDFkkSkbwkrbXFRrVwB1k0tTNU9WIqncOFEgjFfRgR-Z3a2TQ2YrhnmopchWIcFl-YtAfDuhg/" width="291" /></a></b></u></span></span></span></div><div class="separator" style="clear: both; text-align: left;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><u><b><br /></b></u></span></span></span></div><div class="separator" style="clear: both; text-align: left;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><u><b><br /></b></u></span></span></span></div><p></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: #c9211e;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><span style="background: rgb(255, 255, 255);">1.) Calcule as Divisões:</span></b></span></span></span></p><div class="separator" style="clear: both;"><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><br /></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: #c9211e;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><span style="background: rgb(255, 255, 255);">1.) Calcule as Divisões:</span></b></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><br /></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><b><span style="background: rgb(255, 255, 255);">a) (<u> 5 – 3i </u>) =</span></b></span></span></span></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><b style="background-color: white; font-size: 12pt;"> ( 7 + 2i )</b></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><b style="background-color: white; font-size: 12pt;"> </b></p></div><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><span style="color: black;"><span face="HELVETICA, sans-serif"><span style="font-size: 12pt;"><u><b><span style="background: rgb(255, 255, 0);"><br /></span></b></u><b><span style="background: rgb(255, 255, 255);"> b) (<u> 3 – 8i </u>) =</span></b></span></span></span></p><p align="left" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1.15px; margin-bottom: 0.25cm;"><br /> <b style="background-color: white; font-size: 16px;"> (4 – 5i ) </b></p><p align="left" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1.15px; margin-bottom: 0.25cm;"><b style="background-color: white; font-size: 16px;"><br /></b></p><p align="left" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1.15px; margin-bottom: 0.25cm;"><b style="font-size: 16px;"><span style="background: rgb(255, 255, 255);"> c) (<u> 4 + 9i </u>) = </span></b></p><p align="left" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1.15px; margin-bottom: 0.25cm;"><b style="font-size: 16px;"><span style="background: rgb(255, 255, 255);"> </span></b><b style="background-color: white; font-size: 16px;"> ( 5 + 7i )</b></p><p align="left" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1.15px; margin-bottom: 0.25cm;"><b style="background-color: white; font-size: 16px;"><br /></b></p><p align="left" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1.15px; margin-bottom: 0.25cm;"><b style="font-size: 16px;"><span style="background: rgb(255, 255, 255);"> d) (<u> 2 – 3i </u>) =</span></b></p><p align="left" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1.15px; margin-bottom: 0.25cm;"><b style="font-size: 16px;"><span style="background: rgb(255, 255, 255);"> </span></b><b style="background-color: white; font-size: 16px;">( 9 – 6i ) </b></p><p align="left" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1.15px; margin-bottom: 0.25cm;"><b style="font-size: 16px;"><span style="background: rgb(255, 255, 255);"><br /></span></b></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1px; margin-bottom: 0cm;"><br /></p><p align="left" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1.15px; margin-bottom: 0.25cm;"><b style="font-size: 16px;"><span style="background: rgb(255, 255, 255);"><br /></span></b></p><p align="left" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; line-height: 1.15px; margin-bottom: 0.25cm;"><b style="font-size: 16px;"><span style="background: rgb(255, 255, 255);"> </span></b><b style="background-color: white; font-size: 16px;"> </b></p></div>Unknownnoreply@blogger.comtag:blogger.com,1999:blog-6114836858765981739.post-35584837214565941822020-07-30T17:31:00.000-07:002020-07-30T17:31:12.302-07:00ÂNGULOS COMPLEMENTARES<div><br /></div><span class="Apple-style-span" style="color: blue;"><u><b>CONCEITO: </b></u></span>DOIS ÂNGULOS SÃO COMPLEMENTARES QUANDO A SOMA DE SUAS MEDIDAS FOR IGUAL A 90 GRAUS.<br /><br /><b><span class="Apple-style-span" style="color: blue;">EXEMPLO 1:</span></b><br />CALCULANDO O VALOR DE X<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhlJna1nASZlcG5hdTkYy-uQcKV3K6GAI4gAbsa5QfNDyA3pW4CLYZXxXisp-MUsWgXZgvhHCAC8B7xHPrrmySEMRAQEF0ZWt-YB2eYHOJpBdAeR3_j2LkBPLRlhF37KIzLJyBeiiS-NXk/s1600/S.jpg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="181" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhlJna1nASZlcG5hdTkYy-uQcKV3K6GAI4gAbsa5QfNDyA3pW4CLYZXxXisp-MUsWgXZgvhHCAC8B7xHPrrmySEMRAQEF0ZWt-YB2eYHOJpBdAeR3_j2LkBPLRlhF37KIzLJyBeiiS-NXk/s200/S.jpg" width="200" /></a></div><br />CÁLCULO: <b> 50 +</b> <b><span class="Apple-style-span" style="color: blue;">X + </span>10<span class="Apple-style-span" style="color: blue;"> = 90 </span><span class="Apple-style-span" style="color: red;"> ( equação )</span><span class="Apple-style-span" style="color: blue;"> </span></b><br /><b><span class="Apple-style-span" style="color: blue;"> X + </span>60<span class="Apple-style-span" style="color: blue;"> = 90 </span><span class="Apple-style-span" style="color: red; font-family: Arial, Helvetica, sans-serif; font-size: xx-small;">trocando 60 de membro ( inverte a operação )</span></b><br /><span class="Apple-style-span" style="color: blue;"><b> X = 90 - 60</b></span><br /><b><span class="Apple-style-span" style="color: blue;"> </span> X = 30<span class="Apple-style-span" style="color: blue;"> </span></b><br /><b><span class="Apple-style-span" style="color: purple; font-size: x-small;"><br /></span></b><br /><b><span class="Apple-style-span" style="color: purple; font-size: x-small;">VERIFICAÇÃO :</span><span class="Apple-style-span" style="color: blue; font-size: x-small;"> se basta colocar o valor de X = 30 no lugar de X na equação</span></b><br /><b><span class="Apple-style-span" style="font-size: x-small;"> 50 + 30 + 10 = 90 </span></b><br /><b><span class="Apple-style-span" style="color: blue; font-size: x-small;"><br /></span></b><br /><b><span class="Apple-style-span" style="color: blue; font-size: x-small;"><br /></span></b><br /><b><span class="Apple-style-span" style="color: blue;"><br /></span></b><br /><b><span class="Apple-style-span" style="color: blue;">EXEMPLO 2: </span></b><br /><b><span class="Apple-style-span" style="color: blue;"></span></b><span class="Apple-style-span" style="color: blue; font-weight: bold;"> </span>CALCULANDO O VALOR DE X<span class="Apple-style-span" style="color: blue;"> </span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjT0s8SZ7Xfy2KBm-3P1SbTNGemZQsZknieCrlzBWWJITzDr2FPOAYC9Dy5PLVJCV-w8VrDZ3PLUrJFjLbyxAj9QBJmBLiuFUX7742kh5sTaUZtt3BoctsEtv9o0cF9QYowt2g51C_brwk/s1600/T.jpg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="181" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjT0s8SZ7Xfy2KBm-3P1SbTNGemZQsZknieCrlzBWWJITzDr2FPOAYC9Dy5PLVJCV-w8VrDZ3PLUrJFjLbyxAj9QBJmBLiuFUX7742kh5sTaUZtt3BoctsEtv9o0cF9QYowt2g51C_brwk/s200/T.jpg" width="200" /></a></div><b><span class="Apple-style-span" style="color: blue;"><span class="Apple-style-span" style="color: black; font-weight: normal;"></span></span><span class="Apple-style-span" style="color: blue; font-size: x-small;"> </span></b><br /><b><span class="Apple-style-span" style="color: blue; font-size: x-small;"></span></b><b style="font-size: small;">CÁLCULO: 3X</b><span class="Apple-style-span" style="color: red;"><b> +</b></span><b style="font-size: small;"> 60 = 90 </b><span class="Apple-style-span" style="color: red; font-size: x-small; font-weight: bold;">( equação )</span><br /><b style="font-size: small;"> 3X = 90</b><span class="Apple-style-span" style="color: red; font-size: large;"> -</span><b style="font-size: small;"> 60 </b><span class="Apple-style-span" style="color: red; font-size: x-small;">trocando 60 de membro ( inverte a operação ) </span><br /><span class="Apple-style-span" style="font-size: x-small;"><b> 3X = 30 </b></span><br /><b><span class="Apple-style-span" style="font-size: x-small;"> X = 30 : 3 </span></b><br /><b><span class="Apple-style-span" style="font-size: x-small;"> X = 10 </span></b><br /><b><span class="Apple-style-span" style="font-size: x-small;"><span class="Apple-style-span" style="color: purple;">VERIFICAÇÃO</span></span><span class="Apple-style-span" style="color: blue; font-size: x-small;"> </span></b><br /><b><span class="Apple-style-span" style="color: blue; font-size: x-small;"> 3. 10 + 60 = 90 </span></b><br /><b><span class="Apple-style-span" style="color: blue; font-size: x-small;"><br /></span></b><br /><span class="Apple-style-span" style="font-size: x-small;"><b><span class="Apple-style-span" style="color: #38761d;">O MESMO PROCEDIMENTO APLICA-SE EM OUTROS EXEMPLOS</span> </b></span><span class="Apple-style-span" style="color: blue; font-size: x-small; font-weight: bold;"> </span><br /><span class="Apple-style-span" style="color: blue; font-size: x-small; font-weight: bold;"><br /></span><br /><div><span class="Apple-style-span" style="color: blue; font-size: x-small; font-weight: bold;"><u>AGORA FAÇA VOCÊ</u></span></div><span class="Apple-style-span" style="color: blue; font-size: x-small; font-weight: bold;"><br /></span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0zO4HtwMygGWm1-2XKGu0UVJLbeAkBF4f7TAjVQPt6QAhLk9hkqIg_XvFLBDVMTAzi4XGdoxmMKJIXXc-yygfuQU3S3T1LOa6VZu3mYvVLkX-2gIn98SSeGIAxyL3kb1OEENV_dRNayU/s1600/U.jpg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="181" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0zO4HtwMygGWm1-2XKGu0UVJLbeAkBF4f7TAjVQPt6QAhLk9hkqIg_XvFLBDVMTAzi4XGdoxmMKJIXXc-yygfuQU3S3T1LOa6VZu3mYvVLkX-2gIn98SSeGIAxyL3kb1OEENV_dRNayU/s200/U.jpg" width="200" /></a></div><span class="Apple-style-span" style="color: blue; font-size: x-small; font-weight: bold;"><br /></span><br /><span class="Apple-style-span" style="color: blue; font-size: x-small; font-weight: bold;"><br /></span><br /><span class="Apple-style-span" style="color: blue; font-size: x-small; font-weight: bold;"><br /></span><br /><span class="Apple-style-span" style="color: blue; font-size: x-small; font-weight: bold;"><br /></span><br /><span class="Apple-style-span" style="color: blue; font-size: x-small; font-weight: bold;"><br /></span><br /><span class="Apple-style-span" style="color: blue; font-size: x-small; font-weight: bold;"><br /></span><br /><span class="Apple-style-span" style="color: blue; font-size: x-small; font-weight: bold;"><br /></span><br /><span class="Apple-style-span" style="color: blue; font-size: x-small; font-weight: bold;"><br /></span><br /><span class="Apple-style-span" style="color: blue; font-size: x-small; font-weight: bold;"><br /></span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkvO6wRFUPjhIZlnMCFI0IoiUwuizlfUzmKI1NZ-dyzwlbdq7rgwDSd1x3TnhWaWageEu98CH26_6W0U2nFAT3SsavAo-UwbnG-xp8cvoX-Pw6pYtNLVIQylpebmm4xYHsj6m051fxzpc/s1600/V.jpg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="181" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkvO6wRFUPjhIZlnMCFI0IoiUwuizlfUzmKI1NZ-dyzwlbdq7rgwDSd1x3TnhWaWageEu98CH26_6W0U2nFAT3SsavAo-UwbnG-xp8cvoX-Pw6pYtNLVIQylpebmm4xYHsj6m051fxzpc/s200/V.jpg" width="200" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhq0Dx41ep8L7Cs6zpwrI6GsyZ58JvQbZUpuFH4C_wVe97uAM0c5jQmQAdViyb5PZ6CMvxolGNgg7xcgk8NGWgnUSmlWV9C7mUjpQ6Pz80YKv4zegUYep73wW6l2RWx0_hNNWlTsxpauYI/s1600/X.jpg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="181" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhq0Dx41ep8L7Cs6zpwrI6GsyZ58JvQbZUpuFH4C_wVe97uAM0c5jQmQAdViyb5PZ6CMvxolGNgg7xcgk8NGWgnUSmlWV9C7mUjpQ6Pz80YKv4zegUYep73wW6l2RWx0_hNNWlTsxpauYI/s200/X.jpg" width="200" /></a><div><br /></div></div><span class="Apple-style-span" style="color: blue; font-size: x-small;"></span>Unknownnoreply@blogger.comtag:blogger.com,1999:blog-6114836858765981739.post-21893261112419776042020-05-29T10:40:00.001-07:002020-05-29T10:41:44.711-07:00PRISMAS E POLIEDROS GEOMETRIA 6 ANO<div style="text-align: center;">
<img height="640" src="https://atividadespedagogicas.net/wp-content/uploads/2019/03/atividades-poliedros-corpos-redondos-1.png" width="461" /></div>
<img height="640" src="https://atividadespedagogicas.net/wp-content/uploads/2019/03/atividades-poliedros-corpos-redondos-2-1.jpg" width="427" /><br />
<br />Unknownnoreply@blogger.comtag:blogger.com,1999:blog-6114836858765981739.post-11505339498139605342020-05-29T10:37:00.003-07:002020-05-29T10:41:27.780-07:00PRISMAS E POLIEDROS 6 ANO <div style="text-align: center;">
<img alt="atividades com poliedros e corpos redondos" height="640" src="https://atividadespedagogicas.net/wp-content/uploads/2019/03/atividades-poliedros-corpos-redondos-7.jpg" width="438" /></div>
Unknownnoreply@blogger.comtag:blogger.com,1999:blog-6114836858765981739.post-77482341277848462092020-05-26T05:20:00.005-07:002020-08-13T15:22:11.047-07:00AULAS ONLINE<h1 class="noticias-single__title noticias-single__title--desktop visible visible-lg" itemprop="headline" style="background-color: white; box-sizing: border-box; color: #333333; font-family: Merriweather, Georgia, "Times New Roman", Times, serif; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 32px; margin: 10px 0px; text-align: center;">
<u><span style="font-size: x-large;">Aulas online na pandemia: </span></u></h1>
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Veja por que a escola não vai ser mais a mesma</h1>
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Se antes era só levantar a mão para ter a atenção do professor, agora é necessário ativar o microfone da conversa no ambiente virtual de aprendizagem. Nenhuma escola será a mesma de antes. A rotina escolar foi acelerada para um novo tempo e acompanha <a href="https://www.correio24horas.com.br/noticia/nid/nada-sera-como-antes-10-mudancas-que-a-pandemia-ja-provocou-em-sua-vida/" style="background-color: transparent; box-sizing: border-box; color: #57a4ff; font-weight: 700; text-decoration-line: none;">outras revoluções</a> que estão sendo estimuladas pela pandemia, declarada há mais de 50 dias pela Organização Mundial da Saúde (OMS). </div>
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A equação universal professor mais aluno foi dissolvida pelo novo coronavírus. Agora, separada por uma tela, essa dupla tenta se adaptar à uma nova realidade. Segundo a Organização das Nações Unidas para a Educação, a Ciência e a Cultura (Unesco), 191 países fecharam escolas e universidades. Isso significa que 1,6 bilhão de crianças e jovens, ou seja, 90,2% de todos os estudantes do planeta estão - ou já estiveram - sem aulas. Momento desafiador para todos e, no Brasil, não é diferente.</div>
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<img alt="Aula Online ou Presencial: o que é melhor para você? | Focus Concursos" height="225" src="https://blog.focusconcursos.com.br/img/uploads/thumbnails/5c12896a3eea7-scale-1200.jpg" style="background-color: transparent;" width="400" /></div>
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Unknownnoreply@blogger.comtag:blogger.com,1999:blog-6114836858765981739.post-57177587013947027882019-10-18T14:54:00.003-07:002019-10-18T14:55:44.611-07:00ALUNO DESTAQUE 2019.3<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZIqKyYGGmxObWkjXjic-Eb8QoVOfLxCn0vQyOjAZAzVXq1kpSWabSrtT8vQvGIkpOoq-EdMr6jNYhIb_s1xVyN33v4lLIYz1OVcIA9jI93QYrvPqaCAQujoopZ1rvE7lo8ChE5CF4trg/s1600/ALUNO+DESTAQUE+IIUNIDADE+2019.3.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="304" data-original-width="748" height="162" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZIqKyYGGmxObWkjXjic-Eb8QoVOfLxCn0vQyOjAZAzVXq1kpSWabSrtT8vQvGIkpOoq-EdMr6jNYhIb_s1xVyN33v4lLIYz1OVcIA9jI93QYrvPqaCAQujoopZ1rvE7lo8ChE5CF4trg/s400/ALUNO+DESTAQUE+IIUNIDADE+2019.3.png" width="400" /></a></div>
<br />Unknownnoreply@blogger.comtag:blogger.com,1999:blog-6114836858765981739.post-24979422072351289092019-08-14T16:42:00.000-07:002019-08-14T16:42:36.051-07:00ALUNO DESTAQUE CSM 2019.2<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZSye3Byz6AuTAhSBhD9LyNvaONBylBA_YhwxhvucTomrXCswxYv6gXj_2v0_CjcwhW11vueiTknmJ8exPkSO_nTibQc6qKnu7DGiKa4dNUveBc3TkKR7jbil3_qSJoUNwosdnkLFpt-Y/s1600/ALUNO+DESTAQUE+2019.2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="308" data-original-width="750" height="163" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZSye3Byz6AuTAhSBhD9LyNvaONBylBA_YhwxhvucTomrXCswxYv6gXj_2v0_CjcwhW11vueiTknmJ8exPkSO_nTibQc6qKnu7DGiKa4dNUveBc3TkKR7jbil3_qSJoUNwosdnkLFpt-Y/s400/ALUNO+DESTAQUE+2019.2.png" width="400" /></a></div>
<br />Unknownnoreply@blogger.comtag:blogger.com,1999:blog-6114836858765981739.post-68903369458178325762019-07-16T07:03:00.002-07:002019-07-16T07:05:40.636-07:00TURMAS E MÉDIAS<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkh-oiDTi6Bh-nugHoPcCt3gvnfMN5ZvPYV5HmNohv8sGsNrdnCchvpaOX8raU1nnSNJRO6hzUmBkw-t6y1K8qvbA20LvsYG3IcOBnIdI3DEI1NGwGmNGfCCLzYQGOJBRdHQc8nd0lKn4/s1600/GR%25C3%2581FICO+2019+CSM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="469" data-original-width="652" height="287" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkh-oiDTi6Bh-nugHoPcCt3gvnfMN5ZvPYV5HmNohv8sGsNrdnCchvpaOX8raU1nnSNJRO6hzUmBkw-t6y1K8qvbA20LvsYG3IcOBnIdI3DEI1NGwGmNGfCCLzYQGOJBRdHQc8nd0lKn4/s400/GR%25C3%2581FICO+2019+CSM.png" width="400" /></a></div>
<br />Unknownnoreply@blogger.comtag:blogger.com,1999:blog-6114836858765981739.post-6504554981108410952019-05-23T17:28:00.003-07:002019-05-23T17:33:55.076-07:00EQUAÇÃO DO 1º GRAU<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiQMHj9BTvYf8cAxWE5pJ3Y8rfuxaHysSBBbZTtgSf2wtNJ2KP05U8ZyofgGSJHGK_93wH53wrWrgNn4T4VPHoR4iRZUt-L2AH1NOwcYhFnTkXUc-YAsHCzBrUWID_7daLT9MFIGUUEFFg/s1600/EQUA2.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="345" data-original-width="537" height="205" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiQMHj9BTvYf8cAxWE5pJ3Y8rfuxaHysSBBbZTtgSf2wtNJ2KP05U8ZyofgGSJHGK_93wH53wrWrgNn4T4VPHoR4iRZUt-L2AH1NOwcYhFnTkXUc-YAsHCzBrUWID_7daLT9MFIGUUEFFg/s320/EQUA2.jpg" width="320" /></a></div>
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<br />Unknownnoreply@blogger.comtag:blogger.com,1999:blog-6114836858765981739.post-56179081557663682962019-05-17T18:09:00.003-07:002019-05-17T18:09:43.066-07:00EXPOSIÇÃO COMEMORATIVA DIA DA MATEMÁTICA -COLÉGIO SANDRA MARIA -PE<div class="separator" style="clear: both; text-align: center;">
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<br />Unknownnoreply@blogger.comtag:blogger.com,1999:blog-6114836858765981739.post-59492424548809243542019-05-06T07:57:00.000-07:002019-05-06T07:57:06.245-07:00ALUNOS DESTAQUES 2019.1<div class="separator" style="clear: both; text-align: center;">
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<br />Unknownnoreply@blogger.comtag:blogger.com,1999:blog-6114836858765981739.post-59058594220574540302019-03-30T17:09:00.001-07:002019-03-30T17:15:39.347-07:00FIGURAS COM O TANGRAM<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4SgcvjwA8t3O_egWJGlcrswKXRWZpPPI0aa8ccqeYZNy3bxnNBEiIN96THzVKYagTFE8fJ0mVhHDtUA7IZ5Lq9FV7fZ9BCbXlGtTzFwJ6ffsN6HW8ogJaEFokC3UQh88LfjcPPH7Ufhc/s1600/TANGRAM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="479" data-original-width="417" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4SgcvjwA8t3O_egWJGlcrswKXRWZpPPI0aa8ccqeYZNy3bxnNBEiIN96THzVKYagTFE8fJ0mVhHDtUA7IZ5Lq9FV7fZ9BCbXlGtTzFwJ6ffsN6HW8ogJaEFokC3UQh88LfjcPPH7Ufhc/s400/TANGRAM.png" width="347" /></a></div>
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<a href="https://br.pinterest.com/pin/356277020507726300/">https://br.pinterest.com/pin/356277020507726300/</a></div>
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CONSRUÇÃO DO TANGRAM:<a href="https://www.youtube.com/watch?v=dEbGEBwPNAs">https://www.youtube.com/watch?v=dEbGEBwPNAs</a></div>
<br />Unknownnoreply@blogger.comtag:blogger.com,1999:blog-6114836858765981739.post-10657018678822040652019-03-25T06:35:00.001-07:002019-03-25T06:40:45.557-07:00OPERAÇÕES COM NÚMEROS INTEIROS<br />
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;"><u><span style="color: #0070c0;">EXERCÍCIOS 7º <span style="mso-spacerun: yes;"> </span>– MATEMÁTICA</span></u></b><span style="color: #0070c0;"> </span><br />
<br />
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Arial, Helvetica, sans-serif;">1) Determine:</span></b><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">a) O oposto de +6 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">b) O oposto de -9 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">c) O oposto de +6 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">d) O oposto de -6 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">e) O oposto de +18 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">f) O oposto de -15 =</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">g) O oposto de +234= </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">h) O oposto de -1000 =<span style="color: red;"> <o:p></o:p></span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Arial, Helvetica, sans-serif;">2) Qual é o número
maior ?</span></b><br />
<span style="font-family: Arial, Helvetica, sans-serif;">a) +11 ou -10 </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">b) +30 ou 0 </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">c) -20 ou 0 </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">d) +10 ou -10 </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">e) -20 ou -10 </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">f) +20 ou -30 </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">g) -50 ou +50 </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">h) -30 ou -15 <o:p></o:p></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Arial, Helvetica, sans-serif;">3) Compare os
seguites pares de números, dizendo se o primeiro é maior, menor ou igual<br />
</span></b><br />
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b>
<span style="font-family: Arial, Helvetica, sans-serif;">a) +2 e + 4</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">b) +5 e -5 </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">c) -3 e +4 </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">d) +1 e -1 </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">e) -3 e -6 </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">f) -3 e -</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">g) -8 e -2 </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">h) 0 e -5 </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">i) -2 e 0 </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">j) -2 e -4</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">l) -4 e -3 </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">m) 5 e -5 </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">n) 40 e +40 </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">o) -30 e -10 </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">p) -85 e 85 </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">q) 100 e -200 </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">r) -450 e 300 </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">s) -500 e 400 </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Arial, Helvetica, sans-serif;">4) coloque os números em ordem
crescente.</span></b><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">a) -8,-3,-7,+1,0 </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">b) -2, -6, -5, -3, -</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">c) 5,-3,1,0,-1,20</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">d) 25,-3,-18,+15,+8,-9 </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">e) +60,-21,-34,-105,-90</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">f) -400,+620,-840,+1000,-100 </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Arial, Helvetica, sans-serif;">5) Coloque os números em ordem
decrescente</span></b><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">a) +5,-1,-6,+5, </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">b) -4,0,+4,+6,-2 </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">c) -5,1,-3,4, </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">d) +10,+6,-3,-4,-9,+1 </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">e) -18,+83,0,-172, -64 </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">f) -286,-740, +827,0,+904 <o:p></o:p></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Arial, Helvetica, sans-serif;">6) Calcule</span></b><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">a) +6 + 3 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">b) +1 + 4 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">c) -4 - 2 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">d) -3 - 1 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">e) +6 + 9 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">f) +10 + 7 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">g) -8 -12 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">h) -4 -15 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">i) -10 - 15 =</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">j) +5 +18 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">l) -31 - 18 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">m) +20 +40 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">n) -60 - 30 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">o) +75 +15 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">p) -50 -50 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Arial, Helvetica, sans-serif;">7) Calcule:</span></b><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">a) (+4) + (+2) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">b) (+5) + (+1) =</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">c) (+7) + ( +5) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">d) (+2) + (+8) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">e) (+9) + (+4) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">f) (+6) + (+5) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">g) (-3) + (-2) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">h) (-5) + (-1) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">i) (-7) + (-5) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">j) (-4) + (-7) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">l) (-8) + ( -6) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">m) (-5) + ( -6) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Arial, Helvetica, sans-serif;">8) Calcule:</span></b><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">a) ( -12) + ( -19) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">b) (+32) + ( +14) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">c) (-25) + (-25) =</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">d) (-94) + (-18) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">e) (+105) + (+105) =</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">f) (-280) + (-509) =</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">g) (-321) + (-30) = </span><br />
<!--[if !supportLineBreakNewLine]--><span style="font-family: Arial, Helvetica, sans-serif;"><br style="mso-special-character: line-break;" /></span>
<!--[endif]--><span style="color: red; font-family: Arial, Helvetica, sans-serif;"><o:p></o:p></span></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Arial, Helvetica, sans-serif;">9) Calcule:</span></b><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">a) (+19) + (-5) =</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">b) (+3) + (-4) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">c) (-8) + (+6) = <span style="color: red;"><o:p></o:p></span></span></div>
<div class="MsoNormal">
<span style="font-family: Arial, Helvetica, sans-serif;">d) (+5) + (-9) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">e) (-6) + (+2) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">f) (+9) + (-1) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">g) (+8) + (-3) = <span style="color: red;"><o:p></o:p></span></span></div>
<div class="MsoNormal">
<span style="font-family: Arial, Helvetica, sans-serif;">h) (+12) + (-3) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">i) (-7) + (+15) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">j) (-18) + (+8) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">i) (+7) + (-7) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">l) (-6) + 0 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">m) +3 + (-5) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">n) (+2) + (-2) = <span style="color: red;"><o:p></o:p></span></span></div>
<div class="MsoNormal">
<span style="font-family: Arial, Helvetica, sans-serif;">o) (-4) +10 = <span style="color: red;"><o:p></o:p></span></span></div>
<div class="MsoNormal">
<span style="font-family: Arial, Helvetica, sans-serif;">p) -7 + (+9) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">q) +4 + (-12) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">r) +6 + (-4) = <o:p></o:p></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: Arial, Helvetica, sans-serif;"><b style="mso-bidi-font-weight: normal;"><span style="color: #330000;">10) Calcule</span></b><span style="color: #330000;"> </span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="color: #330000; font-family: Arial, Helvetica, sans-serif;">a) 5 + 10 + 8 = </span><br />
<span style="color: #330000; font-family: Arial, Helvetica, sans-serif;">b) 5 - 9 + 1 = </span><br />
<span style="color: #330000; font-family: Arial, Helvetica, sans-serif;">c) -8 - 2 + 3 = </span><br />
<span style="color: #330000; font-family: Arial, Helvetica, sans-serif;">d) -15 + 8 - 7 = </span><br />
<span style="color: #330000; font-family: Arial, Helvetica, sans-serif;">e) 24 + 6 - 12 = </span><br />
<span style="color: #330000; font-family: Arial, Helvetica, sans-serif;">f) -14 - 3 - 6 - 1 = </span><br />
<span style="color: #330000; font-family: Arial, Helvetica, sans-serif;">g) -4 + 5 + 6 + 3 - 9 =</span><br />
<span style="color: #330000; font-family: Arial, Helvetica, sans-serif;">h) -1 + 2 - 4 - 6 - 3 - 8 = </span><br />
<span style="color: #330000; font-family: Arial, Helvetica, sans-serif;">i) 6 - 8 - 3 - 7 - 5 - 1 + 0 - 2 =</span><br />
<span style="color: #330000; font-family: Arial, Helvetica, sans-serif;">j) 2 - 10 - 6 + 14 - 1 + 20 = </span><br />
<span style="color: #330000; font-family: Arial, Helvetica, sans-serif;">L) -13 - 1 - 2 - 8 + 4 - 6 - 10 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<b style="mso-bidi-font-weight: normal;"><span style="color: #330000; font-family: Arial, Helvetica, sans-serif;">11) Efetue,
cancelando os números opostos:</span></b><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="color: #330000; font-family: Arial, Helvetica, sans-serif;">a) 7 + 4 - 6 + 9 - 9 = </span><br />
<span style="color: #330000; font-family: Arial, Helvetica, sans-serif;">b) -7 + 5 - 8 + 7 - 5 = </span><br />
<span style="color: #330000; font-family: Arial, Helvetica, sans-serif;">c) -3 + 5 + 3 - 2 + 2 + 1 = </span><br />
<span style="color: #330000; font-family: Arial, Helvetica, sans-serif;">d) -6 + 10 + 1 - 4 + 6= </span><br />
<span style="color: #330000; font-family: Arial, Helvetica, sans-serif;">e) 10 - 6 + 3 - 3 - 10 - 1 = </span><br />
<span style="color: #330000; font-family: Arial, Helvetica, sans-serif;">f) 15 - 8 + 4 - 4 + 8 - 15 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: #330000;">12) Coloque
em forma simplificada ( sem parênteses)</span><br />
</span></b><br />
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: #330000;"><br /></span></span></b>
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: #330000;">a) (+3) + (+4) +(+2) =</span><span style="color: red;"> <o:p></o:p></span></span></div>
<div class="MsoNormal">
<span style="color: #330000; font-family: Arial, Helvetica, sans-serif;">b) (+1) + (+8) + (-2) = </span><br />
<span style="color: #330000; font-family: Arial, Helvetica, sans-serif;">c) (+5) +(-8) + (-1) = </span><br />
<span style="color: #330000; font-family: Arial, Helvetica, sans-serif;">d) (-6) + (-2) + (+1) =</span><br />
<span style="color: #330000; font-family: Arial, Helvetica, sans-serif;"><br /></span>
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Arial, Helvetica, sans-serif;">13) Calcule:<br />
</span></b><br />
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b>
<span style="font-family: Arial, Helvetica, sans-serif;">a) (+8) - (+3) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">b) (+5) - (-2) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">c) (-3) - ( +8) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">d) (-1) -(-4) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">e) (+3) - (+8) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">f) (+9) - (+9) = <span style="color: red;"><span style="mso-spacerun: yes;"> </span></span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">g) (-8) - ( +5) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">h) (+5) - (-6) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">i) (-2) - (-4) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">j) (-7) - (-8) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">l) (+4) -(+4) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">m) (-3) - ( +2)=</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">n) -7 + 6 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">o) -8 -7 = <span style="color: red;"><o:p></o:p></span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Arial, Helvetica, sans-serif;">14) Calcule:</span></b><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">a) 6 - (-2) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">b) 7 - (+2) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">c) 2 - (-9) =</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">d) -5 - (-1) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">e) -5 -(+1) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">f) -4 - (+3) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">g) 8 - (-5) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">h) 7 - (+4) =</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">i) 26 - 45 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">j) -72 -72 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">l) -84 + 84 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">m) -10 -100 =<span style="color: red;"> </span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">n) -2 -4 -1 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">o) -8 +6 -1 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">p) 12-7 + 3 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">q) 4 + 13 - 21 = <span style="color: red;"><o:p></o:p></span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Arial, Helvetica, sans-serif;">15) Calcule:</span></b><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">a) (-9) -(-2)+(-6) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">b) (-7)-(-5)+(-8) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">c) (+7)-(-6)-(-8) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">d) (-8) + (-6) -(+3) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">e) (-4) + (-3) - (+6) =<span style="color: red;"> </span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">f) 20 - (-6) - (-8) </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">g) 5 - 6 - (+7) + 1 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">h) -10 - (-3) - (-4) </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">i) (+5) + (-8) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">j) (-2) - (-3) =<span style="color: red;"> </span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">l) (-3) -(-9) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">m) (-7) - (-8) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">n) (-8) + (-6) - (-7) </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">o) (-4) + (-6) + (-3) =<span style="color: red;"> </span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">p) 15 -(-3) - (-1) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">q) 32 - (+1) -(-5) =<span style="color: red;"> </span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b style="mso-bidi-font-weight: normal;">16) Elimine os parênteses:<br />
<br />
</b>a) +(-6 +8) = <span style="color: red;"><o:p></o:p></span></span></div>
<div class="MsoNormal">
<span style="font-family: Arial, Helvetica, sans-serif;">b) -(-3 + 8) = <span style="color: red;"><o:p></o:p></span></span></div>
<div class="MsoNormal">
<span style="font-family: Arial, Helvetica, sans-serif;">c) +(5 - 6) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">d) -(-3-1) = <span style="color: red;"><o:p></o:p></span></span></div>
<div class="MsoNormal">
<span style="font-family: Arial, Helvetica, sans-serif;">e) -(-6 + 4 - 1) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">f) +(-3 -2 -1) = <span style="color: red;"><o:p></o:p></span></span></div>
<div class="MsoNormal">
<span style="font-family: Arial, Helvetica, sans-serif;">g) -(4 -6 +8) =</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">h) + (2 + 5 - 1) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Arial, Helvetica, sans-serif;">17) Elimine os parênteses e calcule:</span></b><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">a) + 9 + ( 7 - 3) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">b) 8 - (-2-1) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">c) -6 - (-3 +2) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">d) 18 - ( -5 -2 -3 ) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">e) 30 - (6 - 1 +7) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">f) 4 + (-5 + 0 + 8 -4) </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">g) 4 + (3 - 5) + ( -2 -6) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">h) 8 -(3 + 5 -20) + ( 3 -10) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">i) 20 - (-6 +8) - (-1 + 3) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">j) 35 -(4-1) - (-2 + 7) = <span style="color: red;"><o:p></o:p></span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Arial, Helvetica, sans-serif;">18) Calcule o valor
das seguintes expressões :<br />
</span></b><br />
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b>
<span style="font-family: Arial, Helvetica, sans-serif;">a) 13 -(3-2) + ( 7 -4) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">b) 25 - ( 8 - 5 + 3) - ( 12 - 5 - 8) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">c) ( 10 -2 ) - 3 + ( 8 + 7 - 5) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">d) ( 9 - 4 + 2 ) - 1 + ( 9 + 5 - 3) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">e) 18 - [ 2 + ( 7 - 3 - 8 ) - 10 ] = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">f) -4 + [ -3 + ( -5 + 9 - 2 )] = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">g) -6 - [10 + (-8 -3 ) -1] = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">h) -8 - [ -2 - (-12) + 3 ] = <o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: Arial, Helvetica, sans-serif;">i) 25 - { -2 + [ 6 + ( -4 -1 )]} = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">j) 17 - { 5 - 3 + [ 8 - ( -1 - 3 ) + 5 ] } = </span><br />
<!--[if !supportLineBreakNewLine]--><span style="font-family: Arial, Helvetica, sans-serif;"><br style="mso-special-character: line-break;" /></span>
<!--[endif]--><span style="color: red; font-family: Arial, Helvetica, sans-serif;"><o:p></o:p></span></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Arial, Helvetica, sans-serif;">19) Determine o
produto:</span></b><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">a) (-20) . (+3) . ( +4) =</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">b) (+5) . (-1) . (+2) </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">c) (-6) . (+5) .(-2) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">d) (+8) . (-2) .(-3) =</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">e) (+1) . (+1) . (+1) .(-1)= </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">f) (+3) .(-2) . (-1) . (-5) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">g) (-2) . (-4) . (+6) . (+5) =<span style="color: red;"> </span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">h) (+25) . (-20) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">i) -36) .(-36 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">j) (-12) . (+18) =</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Arial, Helvetica, sans-serif;">20) Calcule os quocientes</span></b><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">a) (+30) : (-5) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">b) (+40) : (+2) =</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">c) (-42) : (+7) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">d) (-32) : (-8)= <o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: Arial, Helvetica, sans-serif;">e) (-75) : (-15) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">f) (-15) : (-15) = <o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: Arial, Helvetica, sans-serif;">g) (-80) : (-10) =<span style="color: red;"> </span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">h) (-48 ) : (+12) =</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">l) (-32) : (-16) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">j) (+60) : (-12) = <o:p></o:p></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Arial, Helvetica, sans-serif;">21) Calcule o valor
das expressões</span></b><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">a) 40 : 2 -7 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">b) -8 + 12 : 3 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">c) 6 : (-2) +1 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">d) 8 : (-4) - (-7) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">e) (-15) : (-3) + 7 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">f) 40 - (-25) : (-5) =</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">g) (-16) : (+4) + 12 = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">h) 18 : 6 + (-28) : (-4) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">i) -14 + 42 : 3 = <span style="color: red;"><o:p></o:p></span></span></div>
<div class="MsoNormal">
<span style="font-family: Arial, Helvetica, sans-serif;">j) 40 : (-2) + 9 = <o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: Arial, Helvetica, sans-serif;">22) Calcule os
quocientes</span></b><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">a) (+60) : (-5) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">b) (+40) : (+2) =</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">c) (-42) : (+7) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">d) (-32) : (-8)= <span style="color: red;"><o:p></o:p></span></span></div>
<div class="MsoNormal">
<span style="font-family: Arial, Helvetica, sans-serif;">e) (-75) : (-15) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">f) (-15) : (-15) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">g) (-80) : (-10) =<span style="color: red;"> </span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">h) (-48 ) : (+12) =</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">l) (-32) : (-16) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">j) (+60) : (-12) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">l) (-64) : (+16) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">m) (-28) : (-14) =<span style="color: red;"> <o:p></o:p></span></span></div>
<div class="MsoNormal">
<span style="font-family: Arial, Helvetica, sans-serif;">n) (0) : (+5) =<span style="color: red;"><o:p></o:p></span></span></div>
<div class="MsoNormal">
<span style="font-family: Arial, Helvetica, sans-serif;">o) 49 : (-7) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">p) 48 : (-6) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">q) (+265) : (-5) =</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">r) (+824) : (+4) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">s) (-180) : (-12) = </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">t) (-480) : (-10) =</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">u) 720 : (-8) =</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">v) (-330) : 15 = </span></div>
<div class="MsoNormal">
<span style="background: white; line-height: 107%;"><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></span></div>
<div class="MsoNormal">
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="background: white; line-height: 107%;"><b><span style="font-family: Courier New, Courier, monospace;">23) Calcule as potencias:</span></b><br />
<br /><span style="font-family: Arial, sans-serif;">
a) (-5)² = </span><br /><span style="font-family: Arial, sans-serif;">
b) (+3)⁴ = </span><br /><span style="font-family: Arial, sans-serif;">
c) (-6)³ = </span><br /><span style="font-family: Arial, sans-serif;">
d) (-1)² = </span><br /><span style="font-family: Arial, sans-serif;">
e) (+10)² = </span><br /><span style="font-family: Arial, sans-serif;">
f) (-3)⁵ = </span><br /><span style="font-family: Arial, sans-serif;">
g) (-1)⁶ = </span></span><span style="line-height: 107%;"><br />
</span><span style="background: white; line-height: 107%;">h) (-1)³ =<br />
i) (+2)⁶ =<br />
j) (-14)² =<br />
k) (-9)² =<br />
l) (-1)⁵⁴ =<br />
m) (-1)¹³ =<br />
n) (-4)³ =<br />
o) (-8)² =<br />
p) (-8)² = </span></span></div>
<div class="MsoNormal">
<span style="background: white; font-family: Arial, Helvetica, sans-serif; line-height: 107%;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="background: white; line-height: 107%;"><b>24) Calcule o valor das expressões
(primeiro as potências):</b><br />
<br />
a) 37 + 6²= </span><span style="line-height: 107%;"><br />
</span><span style="background: white; line-height: 107%;">b) 50 - 4² =<br />
c) -18 + 10² =<br />
d) -6² + 30 =<br />
e) -12-1⁷ =<br />
f) -2⁵ - 40 =<br />
g) 2⁵ + 0 - 2⁴ =<br />
h) 2⁴ - 2² - 2⁰ =<br />
i) -3² + 1 - .65⁰ =<br />
j) 4² - 6 + 0 + 7² =<br />
k) 10 - 7² - 1 + 2³ =<br />
l) 3⁴ - 3³ + 3² - 3¹ + 3⁰ =<br />
<!--[if !supportLineBreakNewLine]--><br />
<!--[endif]--><o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<div class="MsoNormal">
<span style="background: white; font-family: Arial, Helvetica, sans-serif; line-height: 107%;">
<!--[if !supportLineBreakNewLine]--><br />
<!--[endif]--><o:p></o:p></span></div>
<div class="MsoNormal">
<!--[if !supportLineBreakNewLine]--><br style="mso-special-character: line-break;" />
<!--[endif]--><span style="color: red;"><o:p></o:p></span></div>
<br />Unknownnoreply@blogger.comtag:blogger.com,1999:blog-6114836858765981739.post-67202737908574321752019-02-20T13:40:00.001-08:002019-02-20T13:40:18.587-08:00CONJUNTO Z<h3 class="post-title entry-title" itemprop="name" style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 18px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: normal; line-height: normal; margin: 0px; position: relative;">
<br /></h3>
<div class="post-body entry-content" id="post-body-2573972931988722021" itemprop="description articleBody" style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 13.86px; font-weight: 700; line-height: 1.4; position: relative; width: 578px;">
<span style="font-size: 24.948px;"><span style="color: #990000;">OS NÚMEROS INTEIROS</span></span><br /><br /><span style="color: #330099;">Os </span><b style="color: #330099;">números inteiros</b><span style="color: #330099;"> são constituídos dos </span><a class="mw-redirect" href="http://pt.wikipedia.org/wiki/N%C3%BAmeros_naturais" style="color: #330099; text-decoration-line: none;" title="Números naturais">números naturais</a><span style="color: #330099;"> {0, 1, 2, ...} e dos seus simétricos {0, -1, -2, ...}. Dois números são opostos se, e somente se, sua soma é zero. Por vezes, no ensino pré-universitário, chamam-se a estes números </span><i style="color: #330099;">inteiros relativos</i><span style="color: #330099;">.</span><div style="color: red;">
O <a href="http://pt.wikipedia.org/wiki/Conjunto" style="color: #002a77; text-decoration-line: none;" title="Conjunto">conjunto</a> de todos os inteiros é denominado por Z (Mais apropriadamente, um Z em <i><a href="http://pt.wikipedia.org/wiki/Blackboard_bold" style="color: #002a77; text-decoration-line: none;" title="Blackboard bold">blackboard bold</a></i>, <img alt="\mathbb{Z}" class="tex" src="https://blogger.googleusercontent.com/img/proxy/AVvXsEi0Bi1-CVwhZwA2ziSqFLvyW0rp9LqD3BJKRirKE7r2iqmOxH9KreguAYb3rBFYcVVw6es5lwBrYfrW1gIVuamABlUsbtmvUmsJY75lw6GA9O4OQE27KKu24K8txoO05aIf0iAYp7SVcv2J4OljhWzD9zH0-9XKakN9g2VjLzpYZ2z6wMSLjqaFkHR_=s0-d" />), que vem do <a href="http://pt.wikipedia.org/wiki/L%C3%ADngua_alem%C3%A3" style="color: #002a77; text-decoration-line: none;" title="Língua alemã">alemão</a><i>Zahlen</i>, que significa números, algarismos.</div>
<div style="color: #009900;">
Os resultados das operações de soma, subtração e multiplicação entre dois Inteiros são inteiros. Dois inteiros admitem relações binárias como =, > e <.</div>
<div style="color: #666600;">
Matemáticos expressam o facto de que todas as leis usuais da aritmética são válidas nos inteiros dizendo que (Z, +, *) é um <a class="mw-redirect" href="http://pt.wikipedia.org/wiki/Anel_%28%C3%A1lgebra%29" style="color: #002a77; text-decoration-line: none;" title="Anel (álgebra)">anel</a> <a class="mw-redirect" href="http://pt.wikipedia.org/wiki/Comutativo" style="color: #002a77; text-decoration-line: none;" title="Comutativo">comutativo</a>.</div>
<span style="color: blue;">A ordem de Z é dada por ... < -2 < -1 < 0 </span><span style="color: blue; font-size: 13.86px;">< 1 </span><span style="color: blue; font-size: 13.86px;">< 2 ....</span><br />
<span style="color: blue; font-size: 13.86px;"> Chama-se de inteiro</span><span style="color: blue; font-size: 13.86px;"> </span><i style="color: blue; font-size: 13.86px;">positivo</i><span style="color: blue; font-size: 13.86px;"> </span><span style="color: blue; font-size: 13.86px;">os inteiros maiores que zero ; o próprio zero não é considerado um positivo. A ordem é compatível com as operações algébricas no seguinte sentido:</span><br />
<ol>
<li style="margin: 0px 0px 0.25em; padding: 0px;">se <i>a</i> < <i>b</i> e <i>c</i> < <i>d</i>, então <i>a</i> + <i>c</i> < <i>b</i> + <i>d</i></li>
<li style="margin: 0px 0px 0.25em; padding: 0px;">se <i>a</i> < <i>b</i> e 0 < <i>c</i>, então <i>ac</i> < <i>bc</i></li>
</ol>
<div style="color: #cc66cc;">
Como os números naturais, os inteiros formam um conjunto <a href="http://pt.wikipedia.org/wiki/Infinito_cont%C3%A1vel" style="color: #002a77; text-decoration-line: none;" title="Infinito contável">infinito contável</a>.</div>
<div style="color: #ff9900;">
Os inteiros não formam um <a href="http://pt.wikipedia.org/wiki/Corpo" style="color: #002a77; text-decoration-line: none;" title="Corpo">corpo</a> já que, por exemplo, não existe um inteiro <i>x</i> tal que 2<i>x</i> = 1. O menor corpo que contém os inteiros são os <a class="mw-redirect" href="http://pt.wikipedia.org/wiki/N%C3%BAmeros_racionais" style="color: #002a77; text-decoration-line: none;" title="Números racionais">números racionais</a>.</div>
<div style="color: #33ccff;">
Uma importante propriedade dos inteiros é a <i>divisão com resto</i>: dados dois inteiros <i>a</i> e <i>b</i> com <i>b</i>≠0, podemos sempre achar inteiros <i>q</i> e <i>r</i> tais que:<i>a</i> = <i>b</i> <i>q</i> + <i>r</i> e tal que 0 <= <i>r</i> < |<i>b</i>| (veja <a href="http://pt.wikipedia.org/wiki/Valor_absoluto" style="color: #002a77; text-decoration-line: none;" title="Valor absoluto">módulo</a> ou <a href="http://pt.wikipedia.org/wiki/Valor_absoluto" style="color: #002a77; text-decoration-line: none;" title="Valor absoluto">valor absoluto</a>). <i>q</i>é chamado o <i>quociente</i> e <i>r</i> o <i>resto</i> da divisão de <i>a</i> por <i>b</i>. Os números <i>q</i> e <i>r </i>são unicamente determinados por <i>a</i> e <i>b</i>. Esta divisão torna possível o <a href="http://pt.wikipedia.org/wiki/Algoritmo_de_Euclides" style="color: #002a77; text-decoration-line: none;" title="Algoritmo de Euclides">Algoritmo Euclidiano</a> para calcular o <a href="http://pt.wikipedia.org/wiki/M%C3%A1ximo_divisor_comum" style="color: #002a77; text-decoration-line: none;" title="Máximo divisor comum">máximo divisor comum</a>, que também mostra que o máximo divisor comum de dois inteiros pode ser escrito como a soma de múltiplos destes dois inteiros.</div>
<div style="color: red;">
Tudo isto pode ser resumido dizendo que Z é um <a href="http://pt.wikipedia.org/wiki/Dom%C3%ADnio_euclidiano" style="color: #002a77; text-decoration-line: none;" title="Domínio euclidiano">domínio euclidiano</a>. Isto implica que Z é um <a class="new" href="http://pt.wikipedia.org/w/index.php?title=Dom%C3%ADnio_de_ideal_principal&action=edit&redlink=1" style="color: #002a77; text-decoration-line: none;" title="Domínio de ideal principal (página não existe)">domínio de ideal principal</a> e que todo número inteiro podem ser escrito como produto de <a class="mw-redirect" href="http://pt.wikipedia.org/wiki/N%C3%BAmeros_primos" style="color: #002a77; text-decoration-line: none;" title="Números primos">números primos</a> de forma única (desde que o 1 não seja considerado primo).</div>
<div style="color: red;">
Este é o <a class="mw-redirect" href="http://pt.wikipedia.org/wiki/Teorema_Fundamental_da_Aritm%C3%A9tica" style="color: #002a77; text-decoration-line: none;" title="Teorema Fundamental da Aritmética">Teorema Fundamental da Aritmética</a>.</div>
O ramo da <a href="http://pt.wikipedia.org/wiki/Matem%C3%A1tica" style="color: #002a77; text-decoration-line: none;" title="Matemática">matemática</a> que estuda os inteiros é chamado de <a href="http://pt.wikipedia.org/wiki/Teoria_dos_n%C3%BAmeros" style="color: #002a77; text-decoration-line: none;" title="Teoria dos números">teoria dos números</a>.<br />
<h2 style="color: #666666; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: normal; margin: 0.5em 0px; position: relative; text-transform: uppercase;">
<span class="editsection"></span><span class="mw-headline" id="Aplica.C3.A7.C3.A3o">APLICAÇÃO</span></h2>
<div style="color: #ff9900;">
Inteiro é frequentemente um tipo primitivo em <a href="http://pt.wikipedia.org/wiki/Linguagem_de_programa%C3%A7%C3%A3o" style="color: #002a77; text-decoration-line: none;" title="Linguagem de programação">linguagem de programação</a> normalmente com 1, 2, 4, ou 8 <a href="http://pt.wikipedia.org/wiki/Byte" style="color: #002a77; text-decoration-line: none;" title="Byte">bytes</a> de comprimento (8, 16, 32, ou 64 <a class="mw-redirect" href="http://pt.wikipedia.org/wiki/Bits" style="color: #002a77; text-decoration-line: none;" title="Bits">bits</a>). Observe, porem que um computador pode apenas representar um subconjunto dos inteiros com estes tipos, já que os inteiros são infinitos e uma quantidade de bits fixa limita a representação a um máximo de 2 à potência do número de bits (<span class="texhtml">2<sup>8</sup></span> para bytes, <span class="texhtml">2<sup>32</sup></span> para 32-bit arquitecturas, etc). No entanto, o uso de técnicas de <a class="mw-redirect" href="http://pt.wikipedia.org/wiki/Intelig%C3%AAncia_Artificial" style="color: #002a77; text-decoration-line: none;" title="Inteligência Artificial">Inteligência Artificial</a> permitem que computadores representem e raciocinem sobre o conjunto dos inteiros.</div>
</div>
Unknownnoreply@blogger.comtag:blogger.com,1999:blog-6114836858765981739.post-85865318285016605882019-02-20T13:34:00.002-08:002019-02-20T13:34:17.666-08:00A ORIGEM DOS NÚMEROS <div class="MsoNormal" style="background-color: white; font-size: 13.86px; font-weight: 700; line-height: normal;">
<span style="font-size: medium;"><b><span style="color: red; font-family: Arial, Helvetica, sans-serif;">Introdução Sobre a Origem dos Números</span></b></span></div>
<div class="MsoNormal" style="background-color: white; font-size: 13.86px; font-weight: 700; line-height: normal;">
<span style="font-size: medium;"><b><span style="color: red; font-family: Arial, Helvetica, sans-serif;"><br /></span></b></span></div>
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<span style="font-size: 12pt;"><span style="font-family: Arial, Helvetica, sans-serif;">Você já usou muitas vezes os números, mas será que já parou para pensar sobre:</span></span></div>
<ol start="1" style="background-color: white; font-size: 13.86px; font-weight: 700;" type="a">
<li class="MsoNormal" style="line-height: normal; margin: 0px 0px 0.25em; padding: 0px;"><span style="font-size: 12pt;"><span style="font-family: Arial, Helvetica, sans-serif;">O modo como surgiram os números?</span></span></li>
<li class="MsoNormal" style="line-height: normal; margin: 0px 0px 0.25em; padding: 0px;"><span style="font-size: 12pt;"><span style="font-family: Arial, Helvetica, sans-serif;">Como foram as primeiras formas de contagem?</span></span></li>
<li class="MsoNormal" style="line-height: normal; margin: 0px 0px 0.25em; padding: 0px;"><span style="font-size: 12pt;"><span style="font-family: Arial, Helvetica, sans-serif;">Como os números foram criados, ou, será que eles sempre existiram</span></span></li>
</ol>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgH5QsTNlv3uF7QHHzr9dJ1DmNOtn07ok_BdLryg3dcSkV9D7rUrO8Uegegop_lWB6pd9oKkWbuwmDXBzhK5Ffkc7fmTHaPytjRhabVGb67E3rWNcWUSM9nCzyUs5tl5y1LuU2woxs6gQA/s1600/DINO.jpg" imageanchor="1" style="clear: left; color: #002a77; float: left; margin-bottom: 1em; margin-right: 1em; text-decoration-line: none;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgH5QsTNlv3uF7QHHzr9dJ1DmNOtn07ok_BdLryg3dcSkV9D7rUrO8Uegegop_lWB6pd9oKkWbuwmDXBzhK5Ffkc7fmTHaPytjRhabVGb67E3rWNcWUSM9nCzyUs5tl5y1LuU2woxs6gQA/s1600/DINO.jpg" style="border: none; position: relative;" /></span></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><br /><span style="font-size: 12pt;">Para descobrir sobre a origem dos números, precisamos estudar um pouco da história humana e entender os motivos religiosos desses criadores. Na verdade, desconhecemos qualquer outro motivo que tenha gerado os números.</span></span></div>
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<span style="font-size: 12pt;"><span style="font-family: Arial, Helvetica, sans-serif;">Os historiadores são auxiliados por diversas descobertas, como o estudo das ruínas de antigas civilizações, estudos de fósseis, o estudo da linguagem escrita e a avaliação do comportamento de diversos grupos étnicos desde o princípio dos tempos.</span></span></div>
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<span style="font-size: 12pt;"><span style="font-family: Arial, Helvetica, sans-serif;">Olhando ao redor, observamos a grande presença dos números.</span></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRnhPFjJcRx7lOFmsSunplzcF6aq2U9enXOgy9SSHDcGuiMroqt_tbno_vmavgacfEsZiK5XbwkVX2Ow7AaE4RyuN85Xe_WQ2Yf3ydZ2RXi-jeWY1RMqMbdrCl-r2mHgCMmU47GJcEDDQ/s1600/BALA.jpg" imageanchor="1" style="clear: left; color: #002a77; float: left; margin-bottom: 1em; margin-right: 1em; text-decoration-line: none;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="93" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRnhPFjJcRx7lOFmsSunplzcF6aq2U9enXOgy9SSHDcGuiMroqt_tbno_vmavgacfEsZiK5XbwkVX2Ow7AaE4RyuN85Xe_WQ2Yf3ydZ2RXi-jeWY1RMqMbdrCl-r2mHgCMmU47GJcEDDQ/s320/BALA.jpg" style="border: none; position: relative;" width="320" /></span></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><br /><span style="font-size: 12pt;">Quanto mais voltarmos na história, veremos que menor é a presença dos números.</span></span></div>
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<span style="font-size: 12pt;"><span style="font-family: Arial, Helvetica, sans-serif;">O Início do processo de contagem</span></span></div>
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<span style="font-size: 12pt;"><span style="font-family: Arial, Helvetica, sans-serif;">Os homens primitivos não tinham necessidade de contar, pois o que necessitavam para a sua sobrevivência era retirado da própria natureza. A necessidade de contar começou com o desenvolvimento das atividades humanas, quando o homem foi deixando de ser pescador e coletor de alimentos para fixar-se no solo.</span></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjUA-2cZd2q-2tUq7GZ8LxFEYcJtUk3TkQi2hrOYxwy5ePgyv81YPajV2QTGuoQjVfPu8e55FwxIHlnbJKgB0EollLjq5UHZ4TKUQ5RLX3ab4WBp9FFyn7T95yDpTEgsIg20vu6urEeXPg/s1600/OV.jpg" imageanchor="1" style="clear: left; color: #002a77; float: left; margin-bottom: 1em; margin-right: 1em; text-decoration-line: none;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjUA-2cZd2q-2tUq7GZ8LxFEYcJtUk3TkQi2hrOYxwy5ePgyv81YPajV2QTGuoQjVfPu8e55FwxIHlnbJKgB0EollLjq5UHZ4TKUQ5RLX3ab4WBp9FFyn7T95yDpTEgsIg20vu6urEeXPg/s1600/OV.jpg" style="border: none; position: relative;" /></span></a><span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: 12pt;"></span>O homem começou a plantar, produzir alimentos, construir casas, proteções, fortificações e domesticar animais, usando os mesmos para obter a lã e o leite, tornando-se criador de animais domésticos, o que trouxe profundas modificações na vida humana.</span></div>
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<span style="font-size: 12pt;"><span style="font-family: Arial, Helvetica, sans-serif;">As primeiras formas de agricultura de que se tem notícia, foram criadas há cerca de dez mil anos na região que hoje é denominada Oriente Médio.</span></span></div>
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<span style="font-size: 12pt;"><span style="font-family: Arial, Helvetica, sans-serif;">A agricultura passou então a exigir o conhecimento do tempo, das estações do ano e das fases da Lua e assim começaram a surgir as primeiras formas de calendário.</span></span></div>
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<span style="font-size: 12pt;"><span style="font-family: Arial, Helvetica, sans-serif;">No pastoreio, o pastor usava várias formas para controlar o seu rebanho. Pela manhã, ele soltava os seus carneiros e analisava ao final da tarde, se algum tinha sido roubado, fugido, se perdido do rebanho ou se havia sido acrescentado um novo carneiro ao rebanho. Assim eles tinham a correspondência um a um, onde cada carneiro correspondia a uma <i>pedrinha</i> que era armazenada em um saco.</span></span></div>
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<span style="font-size: 12pt;"><span style="font-family: Arial, Helvetica, sans-serif;">No caso das pedrinhas, cada animal que saía para o pasto de manhã correspondia a uma pedra que era guardada em um saco de couro. No final do dia, quando os animais voltavam do pasto, era feita a correspondência inversa, onde, para cada animal que retornava, era retirada uma pedra do saco. Se no final do dia sobrasse alguma pedra, é porque faltava algum dos animais e se algum fosse acrescentado ao rebanho, era só acrescentar mais uma pedra. A palavra que usamos hoje, cálculo, é derivada da palavra latina <i>calculus</i>, que significa pedrinha.</span></span></div>
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<span style="font-size: 12pt;"><span style="font-family: Arial, Helvetica, sans-serif;">A correspondência unidade a unidade não era feita somente com pedras, mas eram usados também nós em cordas, marcas nas paredes, talhes em ossos, desenhos nas cavernas e outros tipos de marcação.</span></span></div>
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<span style="font-size: 12pt;"><span style="font-family: Arial, Helvetica, sans-serif;">Os talhes nas barras de madeira, que eram usados para marcar quantidades, continuaram a ser usados até o século XVIII na Inglaterra. A palavra talhe significa corte. Hoje em dia, usamos ainda a correspondência unidade a unidade.</span></span></div>
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<span style="font-size: 12pt;"><span style="font-family: Arial, Helvetica, sans-serif;">Representação numérica</span></span></div>
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<span style="font-size: 12pt;"><span style="font-family: Arial, Helvetica, sans-serif;">Com o passar do tempo, as quantidades foram representadas por expressões, gestos, palavras e símbolos, sendo que cada povo tinha a sua maneira de representação.</span></span></div>
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<span style="font-size: 12pt;"><span style="font-family: Arial, Helvetica, sans-serif;">A faculdade humana natural de reconhecimento imediato de quantidades se resume a, no máximo, quatro elementos. Este senso numérico que é a faculdade que permite reconhecer que alguma coisa mudou em uma pequena coleção quando, sem seu conhecimento direto, um objeto foi tirado ou adicionado, à coleção.</span></span></div>
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<span style="font-size: 12pt;"><span style="font-family: Arial, Helvetica, sans-serif;">O senso numérico não pode ser confundido com contagem, que é um atributo exclusivamente humano que necessita de um processo mental.</span></span></div>
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<span style="font-size: 12pt;"><span style="font-family: Arial, Helvetica, sans-serif;">"Distingüimos, sem erro e numa rápida vista um, dois, três e mesmo quatro elementos. mas aí para nosso poder de identificação dos números." História Universal dos Algarismos", Georges Ifrah.</span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><br /><span style="color: red; font-size: 18pt; line-height: 27.6px;">A CRIAÇÃO DOS NÚMEROS </span><span style="font-size: 12pt; line-height: 18.4px;"><br /><br />Os números foram inventados pelos homens. Mas sua criação não aconteceu de repente surgiu da necessidade de contar coisas. O homem primitivo, por exemplo, contava traçando riscos na madeira ou no osso, ou ainda, fazendo nós em uma corda. Como era difícil contar quantidades grandes e efetuar cálculos com pedras, nós ou riscos simples, a necessidade de efetuar cálculos com maior rapidez levou o homem a criar símbolos, para representar quantidade. Na antiguidade, nem todos os povos usavam os mesmos símbolos. Vamos conhecer como alguns povos dessa época contavam.<br /></span><span style="color: red; font-size: 18pt; line-height: 27.6px;">A NUNERAÇÃO DOS ROMANOS</span><span style="font-size: 12pt; line-height: 18.4px;"><br /><br />Os romanos representavam quantidades usando as próprias letras de seu alfabeto:<br /><br />I - valia uma unidade<br />V - valia cinco unidades<br />X - representava dez unidades<br />L - indicava cinqüenta unidades<br />C - valia cem unidades<br />D - representava quinhentas unidades<br />M - indicava mil unidades<br /><br />As quantidades eram representadas colocando-se os símbolos uns ao lado dos outros, conforme a seguinte regra:<br /><br />- Os símbolos iguais juntos, até três , significava soma de valores:<br /><br />II = 1 + 1 = 2<br /><br />XXX = 10 + 10 + 10 = 30<br /><br />CCC = 100 + 100 + 100 = 300<br /><br />- Dois símbolos diferentes juntos, com o número menor aparecendo antes do maior, significava subtração de valores:<br /><br />IV = 5 - 1 = 4<br /><br />XL = 50 - 10 = 40<br /><br />XC = 100 - 10 = 90<br /><br />- Dois símbolos diferentes juntos, com o maior aparecendo antes do menor, significa soma de valores:<br /><br />LX = 50 + 10 = 60<br /><br />CCXXX = 200 + 30 = 230<br /><br />DC = 500 + 100 = 600<br /><br />MMMD = 3000 + 500 = 3500<br /><br />- Para indicar quantidades a partir de 4000, os romanos usavam um traço horizontal sobre as letras correspondentes à quantidade de milhares:<br />__<br />IV = 4000<br />_<br />V = 5000<br />_<br />VCCCXX = 5320<br />_____<br />XXIII = 23000<br />obs: Os Romanos não conheciam um símbolo para representar o número zero<br /><br /></span><span style="color: red; font-size: 18pt; line-height: 27.6px;">A NÚMERAÇÃO DOS HINDUS</span><span style="font-size: 12pt; line-height: 18.4px;"><br /><br /><br />Foram os hindus que inventaram os símbolos que usamos até hoje :<br />0,1,2,3,4,5,6,7,8 e 9<br /><br />Esses símbolos, divulgados pelos árabes, são conhecidos como algarismos indo-arábicos e com eles escrevemos todos os números.<br /><br />Mais adiante vamos falar sobre o sistema de numeração que usamos. Você sabe, por exemplo, que 51 e 15 representam quantidades bem diferentes.</span></span></div>
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Unknownnoreply@blogger.comtag:blogger.com,1999:blog-6114836858765981739.post-90629497401054065422018-10-27T17:41:00.002-07:002018-10-27T17:41:31.687-07:00ALUNOS DESTAQUE <div class="separator" style="clear: both; text-align: center;">
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<br />Unknownnoreply@blogger.comtag:blogger.com,1999:blog-6114836858765981739.post-25603264428297523582018-10-19T17:10:00.002-07:002018-10-19T17:13:12.582-07:00RAZÃO E PROPORÇÃO<br />
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Unknownnoreply@blogger.comtag:blogger.com,1999:blog-6114836858765981739.post-51525883669454904132018-09-19T17:40:00.001-07:002018-09-19T17:40:11.150-07:00Sistemas <h3 class="post-title entry-title" itemprop="name" style="background-color: white; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 18px; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: normal; line-height: normal; margin: 0px; position: relative;">
SISTEMAS DE EQUAÇÕES DO 1º GRAU 7º ano</h3>
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<span style="font-size: 13.86px;">Gabarito</span></div>
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<span style="color: blue;"><b>a)</b> (3,2) <b>b)</b> ( 1,2 ) <b>c)</b> ( 15, -22 ) <b> d)</b>4, 1) <b>e) </b>( 4, 3 )</span><br /><b>f)</b> ( 5, -2 ) <b>g)</b> ( -2, 3 ) <b>h) </b>( 3/2, 1) <b> i)</b> ( 2, 0 ) <b> j) </b>( 6, 1 )<br /><span style="color: blue;"><b>k)</b> ( 2, 0) <b>l)</b> ( 1, 2) <b>m) </b>( -1, 1) <b> n)</b> ( 4, 3 ) <b>o)</b> ( -2, 8 )</span><br /><b>p)</b> ( 2, 1) <b>q) </b>(-1, 4) <b> r)</b> ( 0, 5) <b>s)</b> (4, -3) <b>t)</b> ( 17, 14 )<br /><span style="color: blue;"><b>u)</b> ( 5, 4) <b>v)</b> (45, 29) <b>w)</b> ( 7, 4 ) </span></div>
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