Answer
$\frac{9}{10}-\frac{6}{5}i$.
Work Step by Step
The given expression is
$=\frac{6-3i}{4+2i}$
The conjugate of the denominator is $4-2i$.
Multiply the numerator and the denominator by $4-2i$.
$=\frac{6-3i}{4+2i}\cdot \frac{4-2i}{4-2i}$
$=\frac{24-12i-12i+6i^2}{4^2-(2i)^2}$
Use $i^2=-1$.
$=\frac{24-12i-12i-6}{16+4}$
Simplify.
$=\frac{18-24i}{20}$
Rewrite as $a+ib$.
$=\frac{18}{20}-\frac{24}{20}i$
Simplify.
$=\frac{9}{10}-\frac{6}{5}i$.
