Answer
$ 4i$
Work Step by Step
Based on the given conditions, we have:
$[\sqrt 2(cos\frac{5\pi}{8}+i\ sin\frac{5\pi}{8})]^4\\ =4(cos\frac{4*5\pi}{8}+i\ sin\frac{4*5\pi}{8})\\
=4(cos\frac{5\pi}{2}+i\ sin\frac{5\pi}{2})=4i$
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 - Chapter Review - Review Exercises - Page 655: 23
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