Question

A forma algébrica do complexo z= 1 + 3i / 2 - i é:

a) 1/2 - 3i
b) 5/3 + 7/3i
c) -1/5 + 7/5i
d) 3/5 + 4/5i

Answer 1

Olá, cara Baabi.

Dado:

$\boxed{Z= \frac{1+3i}{2-i}}$

Calculando:

$Z= \frac{1+3i(2+i)}{2-i(2+i)} \\ \\ Z= \frac{2+i+6i+3i^2}{4+2i-2i-i^2} \\ \\ Z= \frac{2+7i+3i^2}{4-i^2} \\ \\ Z= \frac{2+7i+3(-1)}{4-i^2} \\ \\ Z= \frac{2+7i-3}{4-(-1)} \\ \\ Z= \frac{-1+7i}{5} \\ \\ \boxed{\boxed{Z= -\frac{1}{5} + \frac{7i}{5}}}$

Obs.: Bons estudos.