Answer
$\frac{107}{101}+\frac{41}{101} i$
Work Step by Step
Rewrite the given expression, and solve the latter. \begin{equation}
\frac{-8-14 i}{-11-9 i} = \frac{8+14 i}{11+9 i}.
\end{equation}Multiply both numerator and denominator by the conjugate of the denominator and simplify.
\begin{equation}
\begin{aligned}
\frac{8+14 i}{11+9 i}&=\frac{8+14 i}{11+9 i}\cdot \frac{(11-9 i)}{(11-9 i)}\\
& =\frac{8(11-9 i)+14i(11-9 i)}{121+81}\\
&=\frac{88-72i+154i+126}{202}\\
&= \frac{214}{202}+\frac{82}{202} i \\
& = \frac{107}{101}+\frac{41}{101} i.
\end{aligned}
\end{equation}
