Answer
$ -\frac{34}{53}+\frac{40}{53} i $
Work Step by Step
Given\begin{equation}
\frac{4+6 i}{2-7 i}.
\end{equation} Multiply both numerator and denominator by conjugate of the denominator and simplify.
\begin{equation}
\begin{aligned}
\frac{4+6 i}{2-7 i}&=\frac{4+6 i}{2-7 i}\cdot \frac{(2+7 i)}{(2+7 i)}\\
& =\frac{4(2+7 i)+6i(2+7 i)}{4+49}\\
&=\frac{8+28i+12i-42}{53}\\
&= -\frac{34}{53}+\frac{40}{53} i \\
\end{aligned}
\end{equation}.
