Answer
$\frac{11}{13}-\frac{16}{13}i$.
Work Step by Step
The given expression is
$=\frac{5-2i}{3+2i}$
The conjugate of the denominator is $3-2i$.
Multiply the numerator and the denominator by $3-2i$.
$=\frac{5-2i}{3+2i}\cdot \frac{3-2i}{3-2i}$
$=\frac{15-10i-6i+4i^2}{3^2-(2i)^2}$
Use $i^2=-1$.
$=\frac{15-10i-6i-4}{9+4}$
Simplify.
$=\frac{11-16i}{13}$
Rewrite as $a+ib$.
$=\frac{11}{13}-\frac{16}{13}i$.
