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: 59

Answer

The graph of all the complex numbers, $z$, will be a unit circle of radius 1 centered at the origin (0,0). It include all the complex numbers of absolute value 1, and each has the equation $|z|$ = 1.

Work Step by Step

For $z = x + yi$, The absolute value of $z$ is 1, shall mean, $|z|$ = 1, or $|z|$ = $\sqrt{x^2 + y^2} = 1$ The graph of all the complex numbers, $z$, satisfying the captioned condition will be a unit circle of radius 1 centered at the origin (0,0). It include all the complex numbers of absolute value 1, and each has the equation $|z|$ = 1.
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