Answer
$-9+40i$
Work Step by Step
We multiply each term of the first complex number with the second complex number and simplify:
$(4+5i)^{2}$
=$(4+5i)(4+5i)$
=$4(4+5i)+5i(4+5i)$
=$16+20i+20i+25i^{2}$
=$16+40i+25(-1)$ [We substitute -1 in place of $i^{2}$ as $i^{2}=-1$]
=$16-25+40i$
=$-9+40i$
