Answer
$\frac{20}{97}+\frac{45}{97}i$
Work Step by Step
Given \begin{equation}
\frac{5}{4-9 i}.
\end{equation} Rationalize the denominator and simplify. \begin{equation}
\begin{aligned}
\frac{5}{4-9 i}&=\frac{5}{4-9 i}\cdot \frac{(4+9i)}{(4+9i)}\\
&= \frac{5(4+9i)}{4^2+9^2}\\
&= \frac{20+45i}{97}\\
&= \frac{20}{97}+\frac{45}{97}i.
\end{aligned}
\end{equation} Hence \begin{equation}
\frac{5}{4-9 i}=\frac{20}{97}+\frac{45}{97}i.
\end{equation}
