Answer
$65+72i$
Work Step by Step
Using $(a+b)^2=a^2+2ab+b^2$ or the square of a binomial, the given expression, $
(9+4i)^2
,$ is equivalent to
\begin{align*}
&
(9)^2+2(9)(4i)+(4i)^2
\\&=
81+72i+16i^2
\\&=
81+72i+16(-1)
&\text{ (use $i^2=-1$)}
\\&=
81+72i-16
.\end{align*}
Combining the real parts, the expression above is equivalent to
\begin{align*}
&
(81-16)+72i
\\&=
65+72i
.\end{align*}
Hence, the simplified form of the given expression is $
65+72i
$.