Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 8 - Quiz (Sections 8.1-8.4) - Page 379: 7d

Answer

$w^3$ = $- 864 - 864\sqrt{3}i$

Work Step by Step

$w = 12(cos80^\circ + isin80^\circ) = 12cis80^\circ$ Now, $w^3$ = $(12cis80^\circ)^3$ = $12^3 cis 3\cdot 80^\circ$ (De Moivre’s Theorem) = $1728cis240^\circ$ = $1728(cos240^\circ + isin240^\circ)$ = $1728(-\frac{1}{2} - \frac{\sqrt{3}}{2} i)$ = $- 864 - 864\sqrt{3}i$
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