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: 47



Work Step by Step

Using De Moivre's Theorem ($(\cos{x}+i\sin{x})^n=\cos{nx}+i\sin{nx}.$): $[\sqrt3(\cos{(10^\circ)}+i(\sin{(10^\circ)})]^6=\sqrt3^6(\cos{(6\cdot10^\circ)}+i(\sin{(6\cdot10^\circ)}))=27\cdot(\cos{(60^\circ)}+i(\sin{(60^\circ})))=27\cdot(\frac{1}{2}+i\frac{\sqrt3}{2})=\frac{27}{2}+i\frac{27\sqrt3}{2}.$
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