Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 8 - 8.6 - Trigonometric Form of a Complex Number - 8.6 Exercises - Page 613: 55



Work Step by Step

DeMoivre's Theorem: If $z=r(cos θ+i~sin θ)$, then $z^n=r^n(cos~nθ+i~sin~nθ)$ $z=(cos~\frac{\pi}{4}+i~sin~\frac{\pi}{4})$ $z^{12}=1^{12}[cos~(12·\frac{\pi}{4})+i~sin~(12·\frac{\pi}{4})]$ $z^{12}=(cos~3\pi+i~sin~3\pi)$ $z^{12}=-1+0i$ $z^{12}=-1$
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