Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 9 - Polar Coordinates; Vectors - 9.3 The Complex Plane; De Moivre's Theorem - 9.3 Assess Your Understanding - Page 594: 44



Work Step by Step

Using De Moivre's Theorem ($(\cos{x}+i\sin{x})^n=\cos{nx}+i\sin{nx}.$): $[3(cos(80^\circ)+i(sin(80^\circ))]^3=3^3(cos(3\cdot80^\circ)+i(sin(3\cdot80^\circ)))=27\cdot(cos(240^\circ)+i(sin(240^\circ)))=27\cdot(-\frac{1}{2}+i\frac{-\sqrt3}{2})=-\frac{27}{2}+i\frac{-27\sqrt3}{2}.$
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