First simplify the equation.

$\frac{1-3\textit{i}}{2+\textit{i}}$

Now multiply by the conjugate.

$\frac{(1-3\textit{i})(2-\textit{i})}{(2-\textit{i})(2+\textit{i})}$

$-\frac{1}{5}+\frac{-7}{5}i$

See part (a).