Answer
$ \frac{17}{29}+\frac{1}{29} i$
Work Step by Step
Given \begin{equation}
\frac{2-4 i}{3-7 i}.
\end{equation} Multiply both numerator and denominator by conjugate of the denominator and simplify.
\begin{equation}
\begin{aligned}
\frac{2-4 i}{3-7 i}&=\frac{2-4 i}{3-7 i}\cdot \frac{(3+7 i)}{(3+7 i)}\\
& =\frac{2(3+7 i)-4i(3+7 i)}{9+49}\\
&=\frac{6+14i-12i+28}{58}\\
&= \frac{34}{58}+\frac{2}{58} i \\
& = \frac{17}{29}+\frac{1}{29} i.
\end{aligned}
\end{equation}
