Answer
$\frac{17}{13}+\frac{7}{13}i$.
Work Step by Step
The given expression is
$=\frac{5-i}{3-2i}$
The conjugate of the denominator is $3+2i$.
Multiply the numerator and the denominator by $3+2i$.
$=\frac{5-i}{3-2i}\cdot \frac{3+2i}{3+2i}$
$=\frac{15+10i-3i-2i^2}{3^2-(2i)^2}$
Use $i^2=-1$.
$=\frac{15+10i-3i+2}{9+4}$
Simplify.
$=\frac{17+7i}{13}$
Rewrite as $a+ib$.
$=\frac{17}{13}+\frac{7}{13}i$.
