Resposta:
[tex]\textsf{Leia abaixo}[/tex]
Explicação passo a passo:
[tex]\mathsf{z = \dfrac{-3 + 2i}{a -i}}[/tex]
[tex]\mathsf{z = \dfrac{-3 + 2i}{a -i}.\dfrac{a + i}{a + i}}[/tex]
[tex]\mathsf{z = \dfrac{-3a - 3i + 2ai + 2i^2}{a^2 - i^2}}[/tex]
[tex]\mathsf{z = \dfrac{-3a - 3i + 2ai + 2(-1)}{a^2 - (-1)}}[/tex]
[tex]\mathsf{z = \dfrac{-3a - 2 + 2ai - 3i}{a^2 + 1}}[/tex]
[tex]\mathsf{z = \dfrac{-3a - 2}{a^2 + 1} + \dfrac{2ai - 3i}{a^2 + 1}}[/tex]
[tex]\mathsf{2ai - 3i = 0}[/tex]
[tex]\mathsf{2ai = 3i}[/tex]
[tex]\boxed{\boxed{\mathsf{a = \dfrac{3}{2}}}}[/tex]
