Question

03) Sendo Z1 = 2 + 2i e Z2 = 1- i, marque a alternativa que corresponde ao valor de: a) 4i b) 2i c) 2 + 2i d) 4 + 4i e) Nenhuma das alternativas.

Answer 1

Explicação passo-a-passo:

$\sf \dfrac{Z_1}{Z_2}=\dfrac{2+2i}{1-i}$

$\sf \dfrac{Z_1}{Z_2}=\dfrac{2+2i}{1-i}\cdot\dfrac{1+i}{1+i}$

$\sf \dfrac{Z_1}{Z_2}=\dfrac{2+2i+2i+2i^2}{1^2-i^2}$

$\sf \dfrac{Z_1}{Z_2}=\dfrac{2+2i+2i+2\cdot(-1)}{1-(-1)}$

$\sf \dfrac{Z_1}{Z_2}=\dfrac{2+2i+2i-2}{1+1}$

$\sf \dfrac{Z_1}{Z_2}=\dfrac{2-2+2i+2i}{2}$

$\sf \dfrac{Z_1}{Z_2}=\dfrac{4i}{2}$

$\sf \dfrac{Z_1}{Z_2}=2i$

Letra B