Answer
$\frac{-27.75+30.3125 i}{30.8125}= -0.9006+0.9838\ i$
Work Step by Step
Given \begin{equation}
\frac{1.5+7.25 i}{3.25-4.5 i}.
\end{equation} First eliminate the decimal and rationalize the denominator.
\begin{equation}
\begin{aligned}
\frac{1.5+7.25 i}{3.25-4.5 i}&=\frac{(1.5+7.25 i)}{(3.25-4.5 i)}\cdot \frac{(3.25+4.5i)}{(3.25+4.5i)}\\
&= \frac{1.5(3.25+4.5i)+7.25i (3.25+4.5i)}{3.25^2+4.5^2}\\
&= \frac{4.875+6.75 i+23.5625 i-32.625}{30.8125}\\
&= \frac{-27.75+30.3125 i}{30.8125}\\
&\approx -0.9006+0.9838\ i.
\end{aligned}
\end{equation} The answer is: \begin{equation}
\frac{-27.75+30.3125 i}{30.8125}= -0.9006+0.9838\ i.
\end{equation}
