Answer
$-\frac{29}{85}+\frac{82}{85} i $
Work Step by Step
Rewrite the given expression, and solve the latter.
\begin{equation}
\frac{-8-5 i}{-2+9 i}= (-1)\cdot \frac{-8-5i}{2-9i} = \frac{8+5i}{2-9i}.
\end{equation} Multiply both numerator and denominator by the conjugate of the denominator and simplify.
\begin{equation}
\begin{aligned}
\frac{8+5i}{2-9i}&=\frac{8+5i}{2-9i}\cdot \frac{(2+9i)}{(2+9i)}\\
& =\frac{8(2+9i)+5i(2+9i)}{4+81}\\
&=\frac{16+72i+10i-45}{85}\\
&= -\frac{29}{85}+\frac{82}{85} i.
\end{aligned}
\end{equation}
