Answer
$-\frac{23}{58}+\frac{43}{58}i$.
Work Step by Step
The given expression is
$=\frac{4+5i}{3-7i}$
The conjugate of the denominator is $3+7i$.
Multiply the numerator and the denominator by $3+7i$.
$=\frac{4+5i}{3-7i}\cdot \frac{3+7i}{3+7i}$
$=\frac{12+28i+15i+35i^2}{3^2-(7i)^2}$
Use $i^2=-1$.
$=\frac{12+28i+15i-35}{9+49}$
Simplify.
$=\frac{-23+43i}{58}$
Rewrite as $a+ib$.
$=-\frac{23}{58}+\frac{43}{58}i$.
