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: 48



Work Step by Step

Using De Moivre's Theorem ($(\cos{x}+i\sin{x})^n=\cos{nx}+i\sin{nx}.$): $[0.5(\cos{(72^\circ)}+i(\sin{(72^\circ}))]^5=0.5^5(\cos{(5\cdot72^\circ)}+i(\sin{(5\cdot72^\circ})))=\frac{1}{32}\cdot(\cos{(360^\circ)}+i(\sin{(360^\circ})))=\frac{1}{32}\cdot(1+0)=\frac{1}{32}.$
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