Answer
$ \frac{1}{32}$
Work Step by Step
Based on the given conditions, we have:
$[\frac{1}{2}(cos72^\circ+i\ sin72^\circ)]^5\\ =\frac{1}{32}(cos(5)72^\circ+i\ sin(5)72^\circ)\\ =\frac{1}{32}(cos360^\circ+i\ sin360^\circ) =\frac{1}{32}$
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: 46
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