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: 56



Work Step by Step

DeMoivre's Theorem: If $z=r(cos θ+i~sin θ)$, then $z^n=r^n(cos~nθ+i~sin~nθ)$ $z=2(cos~\frac{\pi}{2}+i~sin~\frac{\pi}{2})$ $z^8=2^8[cos~(8·\frac{\pi}{2})+i~sin~(8·\frac{\pi}{2})]$ $z^8=256(cos~4\pi+i~sin~4\pi)$ $z^8=256(1+0i)$ $z^8=256$
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