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