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: 72

Answer

If $z = cos\theta - isin\theta$, then its absolute value $|z|$ = 1 (As proved in the step by step work)

Work Step by Step

If $z = cos\theta - isin\theta$, its absolute value $|z|$ will be, = $\sqrt{cos^2\theta + (-sin\theta)^2}$ = $\sqrt{cos^2\theta + sin^2\theta}$ = 1 (since according to Pythagorean identity, $cos^2\theta + sin^2\theta = 1$) Hence, if $z = cos\theta - isin\theta$, then its absolute value $|z|$ = 1.
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