Answer
$\frac{6073}{7813}+\frac{62}{7813}\ i\approx 0.777+0.008 i$
Work Step by Step
Given \begin{equation}
\frac{2.5+6.4 i}{3.3+8.2 i}.
\end{equation} First eliminate the decimal and rationalize the denominator.
\begin{equation}
\begin{aligned}
\frac{2.5+6.4 i}{3.3+8.2 i}&= \frac{(2.5+6.4 i)}{(3.3+8.2 i)}\cdot \frac{10}{10}\\
& = \frac{(25+64 i)}{(33+82 i)}\cdot \frac{(33-82i)}{(33-82i)}\\
&= \frac{25(33-82i)+64i (33-82i)}{33^2+82^2}\\
&= \frac{825-2050i+2112i+5248}{7813}\\
&= \frac{6073}{7813}+\frac{62}{7813}\ i\\
&\approx 0.777+0.008 i.
\end{aligned}
\end{equation} The answer is: \begin{equation}
\frac{6073}{7813}+\frac{62}{7813}\ i\approx 0.777+0.008 i.
\end{equation}
