Trigonometry (10th Edition)

by Lial, Margaret L.; Hornsby, John; Schneider, David I.; Daniels, Callie

Published by Pearson

ISBN 10: 0321671775

ISBN 13: 978-0-32167-177-6

Chapter 8 - Review Exercises - Page 404: 27

Answer

$(cos100^\circ + isin100^\circ)^6$ = $-\frac{1}{2} - \frac{\sqrt{3}}{2}i$

Work Step by Step

$(cos100^\circ + isin100^\circ)^6$ = $cos6\cdot 100^\circ + isin6\cdot 100^\circ$ (De Moivre’s Theorem) = $cos600^\circ + isin600^\circ$ = $-\frac{1}{2} - \frac{\sqrt{3}}{2}i$

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