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: 64a

Answer

The complex conjugates of $z$ have the same absolute value.

Work Step by Step

For $z = a + bi$, the absolute value of $z$ is $\sqrt{a^2 + b^2}$, while, for the conjugate of $z$, $\bar{z} = a - bi$, the absolute value of $\bar{z}$ is $\sqrt{a^2 + (-b)^2}$, which is also equal to $\sqrt{a^2 + b^2}$ Therefore, the complex conjugates of $z$ have the same absolute value.
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