Question

03) Sendo Z1 = 4 + 2i e Z2 = 1 + i, marque a alternativa que corresponde ao valor de: *

$\frac{z1}{z2}$


3 - i

3 + i

2 - i

2 + i

Nenhuma das alternativas.

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Answer 1

Explicação passo-a-passo:

$\sf \dfrac{z_1}{z_2}=\dfrac{4+2i}{1+i}$

$\sf \dfrac{z_1}{z_2}=\dfrac{4+2i}{1+i}\cdot\dfrac{1-i}{1-i}$

$\sf \dfrac{z_1}{z_2}=\dfrac{4+2i-4i-2i^2}{1^2-i^2}$

$\sf \dfrac{z_1}{z_2}=\dfrac{4+2i-4i-2\cdot(-1)}{1-(-1)}$

$\sf \dfrac{z_1}{z_2}=\dfrac{4+2i-4i+2}{1+1}$

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

$\sf \dfrac{z_1}{z_2}=\dfrac{6-2i}{2}$

$\sf \dfrac{z_1}{z_2}=3-i$