Answer
$\frac{1}{5}+\frac{11}{10}i$.
Work Step by Step
The given expression is
$=\frac{3+4i}{4-2i}$
The conjugate of the denominator is $4+2i$.
Multiply the numerator and the denominator by $4+2i$.
$=\frac{3+4i}{4-2i}\cdot \frac{4+2i}{4+2i}$
Use the special formula $(A+B)^2=A^2+2AB+B^2$
$=\frac{12+6i+16i+8i^2}{(4)^2-(2i)^2}$
Use $i^2=-1$.
$=\frac{12+22i-8}{16+4}$
Simplify.
$=\frac{4+22i}{20}$
Rewrite as $a+ib$.
$=\frac{4}{20}+\frac{22}{20}i$
Simplify.
$=\frac{1}{5}+\frac{11}{10}i$.
