Question

06) Sendo Z1 = 2 - 2i e Z2 = 1 + i, marque a alternativa que corresponde ao valor de: *

$\frac{z1}{z2}$


2i

-2i

-2i/2

2i/2

Nenhuma das alternativas.

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Answer 1

Explicação passo-a-passo:

$\sf \dfrac{z_1}{z_2}=\dfrac{2-2i}{1+i}$

$\sf \dfrac{z_1}{z_2}=\dfrac{2-2i}{1+i}\cdot\dfrac{1-i}{1-i}$

$\sf \dfrac{z_1}{z_2}=\dfrac{2-2i-2i+2i^2}{1^2-i^2}$

$\sf \dfrac{z_1}{z_2}=\dfrac{2-2i-2i+2\cdot(-1)}{1-(-1)}$

$\sf \dfrac{z_1}{z_2}=\dfrac{2-2i-2i-2}{1+1}$

$\sf \dfrac{z_1}{z_2}=\dfrac{2-2-2i-2i}{2}$

$\sf \dfrac{z_1}{z_2}=\dfrac{-4i}{2}$

$\sf \dfrac{z_1}{z_2}=-2i$