Answer
$-5+12i$
Work Step by Step
$\text{Solution:}$
Step 1: $(2+3i)^2=(2+3i)(2+3i) ~~~~~~\because a^2=a\times a$
Step 2: Multiplication of complex numbers works just like for polynomials
\begin{align*}(2+3i)(2+3i)=&2(2+3i)+3i(2+3i)\\
=&2(2)+2(3i)+3i(2)+3i(3i)~~~\text{Simplify}\\
=&4+6i+6i+9i^2\\
=&4+12i+9(-1) ~~~~\because i^2=-1\\
=&4-9+12~~~~~\text{Simplify}\\
=&-5+12i.
\end{align*}
Step3: The Cartesian form of $(2+3i)^2$ is $-5+12i$.
