Answer
$\text{True }$
Work Step by Step
Note that:
\begin{align*}
(a+ib)(a-bi)&=a^2-b^2i^2&\\
&=a^2-b^2(-1)\\
&=a^2+b^2\end{align*}
Since both $a^2$ and $b^2$ are non-negative, then the given statement is true.
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
Published by
Pearson
ISBN 10:
0-32193-104-1
ISBN 13:
978-0-32193-104-7
Appendix A - Review - A.11 Complex Numbers - A.11 Assess Your Understanding - Page A94: 8
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