Question

Qual deve ser o valor de A para que o número complexo Z = -3+2i/a-i seja real?​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{z = \dfrac{-3 + 2i}{a -i}}$

$\mathsf{z = \dfrac{-3 + 2i}{a -i}.\dfrac{a + i}{a + i}}$

$\mathsf{z = \dfrac{-3a - 3i + 2ai + 2i^2}{a^2 - i^2}}$

$\mathsf{z = \dfrac{-3a - 3i + 2ai + 2(-1)}{a^2 - (-1)}}$

$\mathsf{z = \dfrac{-3a - 2 + 2ai - 3i}{a^2 + 1}}$

$\mathsf{z = \dfrac{-3a - 2}{a^2 + 1} + \dfrac{2ai - 3i}{a^2 + 1}}$

$\mathsf{2ai - 3i = 0}$

$\mathsf{2ai = 3i}$

$\boxed{\boxed{\mathsf{a = \dfrac{3}{2}}}}$