Answer
False.
Work Step by Step
The given expression is
$=\frac{7+3i}{5+3i}$
The conjugate of the denominator is $5-3i$.
Multiply the numerator and the denominator by $5-3i$.
$=\frac{7+3i}{5+3i}\cdot \frac{5-3i}{5-3i}$
Use the special formula $(A+B)^2=A^2+2AB+B^2$
$=\frac{35-21i+15i-9i^2}{5^2-(3i)^2}$
Use $i^2=-1$.
$=\frac{35-21i+15i+9}{25+9}$
Simplify.
$=\frac{44-6i}{34}$
Rewrite as $a+ib$.
$=\frac{44}{34}-\frac{6}{34}i$
Simplify.
$=\frac{22}{17}-\frac{3}{17}i$.
Hence, the given statement is false.
