Answer
$7+24i$
Work Step by Step
Using $(a+b)^2=a^2+2ab+b^2$ and that $i^2=-1,$ the given expression, $
(4+3i)^2
,$ is equivalent to
\begin{array}{l}\require{cancel}
(4)^2+2(4)(3i)+(3i)^2
\\\\=
16+24i+9i^2
\\\\=
16+24i+9(-1)
\\\\=
16+24i-9
\\\\=
7+24i
.\end{array}
