Answer
$5+12i$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
(3+2i)^2
,$ use the special product on squaring binomials. Then use $i^2=-1$ and combine like terms.
$\bf{\text{Solution Details:}}$
Using the square of a binomial which is given by $(a+b)^2=a^2+2ab+b^2$ or by $(a-b)^2=a^2-2ab+b^2,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
(3)^2+2(3)(2i)+(2i)^2
\\\\=
9+12i+4i^2
.\end{array}
Since $i^2=-1,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
9+12i+4(-1)
\\\\=
9+12i-4
.\end{array}
Combining like terms results to
\begin{array}{l}\require{cancel}
(9-4)+12i
\\\\=
5+12i
.\end{array}
