Answer
$\frac{61}{34}-\frac{11}{34} i$
Work Step by Step
Rewrite the given expression, and solve the latter. \begin{equation}
\frac{-7-8 i}{-3-5 i}= \frac{7+8 i}{3+5 i}.
\end{equation} Multiply both numerator and denominator by the conjugate of the denominator and simplify.
\begin{equation}
\begin{aligned}
\frac{7+8 i}{3+5 i}&=\frac{7+8 i}{3+5 i}\cdot \frac{(3-5 i)}{(3-5 i)}\\
& =\frac{7(3-5 i)+8i(3-5 i)}{9+25}\\
&=\frac{21-35i+24i+40}{34}\\
&= \frac{61}{34}-\frac{11}{34} i.
\end{aligned}
\end{equation} We got \begin{equation}
\frac{-7-8 i}{-3-5 i}= \frac{61}{34}-\frac{11}{34} i.
\end{equation}
