Answer
$ \frac{46}{73}+\frac{1}{73}i$
Work Step by Step
Given \begin{equation}
\frac{2-5 i}{3-8 i}.
\end{equation} Rationalize the denominator and simplify.
\begin{equation}
\begin{aligned}
\frac{2-5 i}{3-8 i}&=\frac{(2-5 i)}{(3-8 i)}\cdot \frac{(3+8i)}{(3+8i)}\\
&= \frac{2(3+8i)-5i(3+8i)}{3^2+8^2}\\
&= \frac{6+16i-15i+40}{73}\\
&= \frac{46+i}{73}\\
&= \frac{46}{73}+\frac{1}{73}i.
\end{aligned}
\end{equation} Hence \begin{equation}
\frac{2-5 i}{3-8 i}= \frac{46}{73}+\frac{1}{73}i.
\end{equation}
