Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.2 Trigonometric (Polar) Form of Complex Numbers - 8.2 Exercises - Page 365: 65

Answer

The conjugate of z is $\bar{z}$ = $r(cos\theta - i\cdot sin\theta)$ or $r[cos(360^\circ - \theta) + i\cdot sin(360^\circ - \theta)]$

Work Step by Step

For $z = r(cos\theta + i\cdot sin\theta)$, or in rectangular form, $z = a + bi$, By comparing, $a = rcos\theta$ and $b = rsin\theta$ As the conjugate of $z$ is $\bar{z} = a - bi$, $\bar{z}$ = $a - bi$ = $rcos\theta - i\cdot rsin\theta$ = $r(cos\theta - i\cdot sin\theta)$
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