Answer
$ -64$
Work Step by Step
Based on the given conditions, we have:
$(\sqrt 3-i)^6\\ =[2(cos\frac{5\pi}{6}+i\ sin\frac{5\pi}{6})]^6\\ =64(cos5\pi+i\ sin5\pi)\\ =64(-1+0i)\\ =-64$
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
Published by
Pearson
ISBN 10:
0-32193-104-1
ISBN 13:
978-0-32193-104-7
Chapter 8 - Polar Coordinates; Vectors - Section 8.3 The Complex Plane; De Moivre's Theorem - 8.3 Assess Your Understanding - Page 615: 50
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