Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 8 - Section 8.2 - Trigonometric Form for Complex Numbers - 8.2 Problem Set - Page 433: 69

Answer

$2cis30^\circ$ and $2cis(-30^\circ)$ are conjugates (As proved in the step by step work)

Work Step by Step

$2cis30^\circ$ = $2(cos30^\circ + isin30^\circ)$ $2cis(-30^\circ)$ = $2[cos(-30^\circ) + isin(-30^\circ)]$ = $2(cos30^\circ - isin30^\circ)$ (since $cos(-\theta) = cos\theta$ and $sin(-\theta) = -sin\theta$) Hence, $2cis30^\circ$ and $2cis(-30^\circ)$ are conjugates.
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