Answer
$\frac{41}{29}-\frac{1}{29} i$
Work Step by Step
Given \begin{equation}
\frac{3+7 i}{2+5 i}.
\end{equation} Multiply both numerator and denominator by the conjugate of the denominator and simplify.
\begin{equation}
\begin{aligned}
\frac{3+7 i}{2+5 i}&=\frac{3+7 i}{2+5 i}\cdot \frac{(2-5 i)}{(2-5 i)}\\
& =\frac{3(2-5 i)+7i(2-5 i)}{4+25}\\
&=\frac{6-15 i+14i+35}{29}\\
&= \frac{41}{29}-\frac{1}{29} i.
\end{aligned}
\end{equation} We got $$\frac{3+7 i}{2+5 i}=\frac{41}{29}-\frac{1}{29} i.$$
