Question

1. dados os números z1 =3+2i,z2= 2+5i e z3= 1-i calcule
a)z1+z2
b)z2+z3
c)z2-z1
d)z3-z2
e)z3-z1
f)z1×z3
g)z2×z3​

Answer 1

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$\large\green{\boxed{\rm~~~\red{ A)}~\gray{z_1 + z_2}~\pink{=}~\blue{ 5 + 7i }~~~}}$

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$\large\green{\boxed{\rm~~~\red{ B)}~\gray{z_2 + z_3}~\pink{=}~\blue{ 3 + 4i }~~~}}$

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$\large\green{\boxed{\rm~~~\red{ C)}~\gray{z_2 - z_1}~\pink{=}~\blue{ -1 + 3i }~~~}}$

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$\large\green{\boxed{\rm~~~\red{ D)}~\gray{z_3 - z_2}~\pink{=}~\blue{ -1 - 6i }~~~}}$

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$\large\green{\boxed{\rm~~~\red{ E)}~\gray{z_3 - z_1}~\pink{=}~\blue{ -2 - 3i }~~~}}$

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$\large\green{\boxed{\rm~~~\red{ F)}~\gray{z_1 \times z_3}~\pink{=}~\blue{ 5 - i }~~~}}$

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$\large\green{\boxed{\rm~~~\red{ G)}~\gray{z_2 \times z_3}~\pink{=}~\blue{ 4 + 3i }~~~}}$

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$\bf\large\green{\underline{\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad}}$

$\green{\rm\underline{EXPLICAC_{\!\!\!,}\tilde{A}O\ PASSO{-}A{-}PASSO\ \ \ }}$✍

❄☃ $\sf(\gray{+}~\red{cores}~\blue{com}~\pink{o}~\orange{App}~\green{Brainly})$ ☘☀

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☺lá novamente, Ana. Vamos a mais um exercício❗ A resolução abaixo foi feita basicamente colocando em evidência os termos em comum para em seguida realizarmos a operação. Nos últimos dois itens teremos uma multiplicação de binômios. Após a resolução você encontrará um link com um resumo sobre Manipulação Algébrica que talvez te ajude com exercícios semelhantes no futuro. ✌

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Ⓐ$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\quad}}$✍

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$\large\gray{\boxed{\rm\blue{ z_1 + z_2 }}}$

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$\large\sf\blue{ = 3 + 2i + 2 + 5i}$

$\large\sf\blue{ = 5 + 7i}$

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$\large\green{\boxed{\rm~~~\red{ A)}~\gray{z_1 + z_2}~\pink{=}~\blue{ 5 + 7i }~~~}}$ ✅

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Ⓑ$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\quad}}$✍

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$\large\gray{\boxed{\rm\blue{ z_2 + z_3 }}}$

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$\large\sf\blue{ = 2 + 5i + 1 - i}$

$\large\sf\blue{ = 3 + 4i}$

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$\large\green{\boxed{\rm~~~\red{ B)}~\gray{z_2 + z_3}~\pink{=}~\blue{ 3 + 4i }~~~}}$ ✅

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Ⓒ$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\quad}}$✍

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$\large\gray{\boxed{\rm\blue{ z_2 - z_1 }}}$

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$\large\sf\blue{ = 2 + 5i - (3 + 2i)}$

$\large\sf\blue{ = 2 + 5i - 3 - 2i}$

$\large\sf\blue{ = -1 + 3i}$

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$\large\green{\boxed{\rm~~~\red{ C)}~\gray{z_2 - z_1}~\pink{=}~\blue{ -1 + 3i }~~~}}$ ✅

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Ⓓ$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\quad}}$✍

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$\large\gray{\boxed{\rm\blue{ z_3 - z_2 }}}$

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$\large\sf\blue{ = 1 - i -(2 + 5i)}$

$\large\sf\blue{ = 1 - i - 2 - 5i}$

$\large\sf\blue{ = -1 - 6i}$

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$\large\green{\boxed{\rm~~~\red{ D)}~\gray{z_3 - z_2}~\pink{=}~\blue{ -1 - 6i }~~~}}$ ✅

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Ⓔ$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\quad}}$✍

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$\large\gray{\boxed{\rm\blue{ z_3 - z_1 }}}$

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$\large\sf\blue{ = 1 - i -(3 + 2i)}$

$\large\sf\blue{ = 1 - i - 3 - 2i}$

$\large\sf\blue{ = -2 - 3i}$

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$\large\green{\boxed{\rm~~~\red{ E)}~\gray{z_3 - z_1}~\pink{=}~\blue{ -2 - 3i }~~~}}$ ✅

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Ⓕ$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\quad}}$✍

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$\large\gray{\boxed{\rm\blue{ z_1 \times z_3 }}}$

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$\large\sf\blue{ = (3 + 2i) \times (1 - i)}$

$\large\sf\blue{ = 3 \times (1 - i) + 2i \times (1 - i)}$

$\large\sf\blue{ = 3 - 3i + 2i - 2 \times (i^2)}$

$\large\sf\blue{ = 3 - i - 2 \times (-1)}$

$\large\sf\blue{ = 3 - i + 2 }$

$\large\sf\blue{ = 5 - i }$

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$\large\green{\boxed{\rm~~~\red{ F)}~\gray{z_1 \times z_3}~\pink{=}~\blue{ 5 - i }~~~}}$ ✅

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Ⓖ$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\quad}}$✍

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$\large\gray{\boxed{\rm\blue{ z_2 \times z_3 }}}$

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$\large\sf\blue{ = (2 + 5i) \times (1 - i)}$

$\large\sf\blue{ = 2 \times (1 - i) + 5i \times (1 - i)}$

$\large\sf\blue{ = 2 - 2i + 5i - 5 \times (i^2)}$

$\large\sf\blue{ = 2 + 3i - 2 \times (-1)}$

$\large\sf\blue{ = 2 + 3i + 2 }$

$\large\sf\blue{ = 4 + 3i }$

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$\large\green{\boxed{\rm~~~\red{ G)}~\gray{z_2 \times z_3}~\pink{=}~\blue{ 4 + 3i }~~~}}$ ✅

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$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$

✈  Manipulação Algébrica (https://brainly.com.br/tarefa/37266101)

$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad}}$✍

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$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$☁

☕ $\bf\large\blue{Bons\ estudos.}$

($\orange{D\acute{u}vidas\ nos\ coment\acute{a}rios}$) ☄

$\bf\large\red{\underline{\qquad \qquad \qquad \qquad \qquad \qquad \quad }}\LaTeX$✍

❄☃ $\sf(\gray{+}~\red{cores}~\blue{com}~\pink{o}~\orange{App}~\green{Brainly})$ ☘☀

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$\gray{"Absque~sudore~et~labore~nullum~opus~perfectum~est."}$