College Algebra, Chapter 1, 1.4, Section 1.4, Problem 26

Evaluate the expression $(5 - 3i)(1 + i)$ in the form of $a + bi$.


$
\begin{equation}
\begin{aligned}
&= (5 - 3i)(1 + i) && \text{Using FOIL method}\\
\\
&= 5 + 5i - 3i - 3i^2 && \text{recall that } i^2 = -1\\
\\
&= 5 + 5i - 3i -3 (-1) && \text{combine like terms}\\
\\
&= 8+2i
\end{aligned}
\end{equation}
$