Answer
$\frac{3}{10}+\frac{11}{10}i$
Work Step by Step
Start by multiplying the numerator and the denominator by the complex conjugate of the denominator as shown below.
\begin{equation}
\begin{aligned}
& \frac{2+3 i}{3-i}=\frac{(2+3 i)}{(3-i)}\cdot \frac{(3+i)}{(3+i)} \\
& =\frac{2(3+i)+3 i(3+i)}{3^2+1^2} \\
& =\frac{6+2 i+9 i+3 i^2}{10} \\
& =\frac{6+11 i-3}{10} \ ;\ i^2=-1\\
& =\frac{3}{10}+\frac{11}{10}i\\
\end{aligned}
\end{equation}
