Answer
$44+6i$.
Work Step by Step
Use the FOIL method to multiply $5+3i$ and $7-3i$.
$(5+3i)(7-3i)$
$=5\cdot 7+5\cdot (-3i)+(3i)\cdot 7+(3i)\cdot (-3i)$
$=35-15i+21i-9i^2$
$=35+6i-9i^2$
Use $i^2=-1$.
$=35+6i-9(-1)$
$=35+6i+9$
Simplify.
$=44+6i$.
