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: 64e

Answer

As real conjugates are symmetric across the imaginary y-axis, the Julia set must be symmetric with respect to the imaginary y-axis too.

Work Step by Step

For $z = a + bi$, real conjugate of $z$ is -a + bi. Same like complex conjugates, real conjugates also have the same absolute values. As real conjugates are symmetric across the imaginary y-axis, the Julia set must be symmetric with respect to the imaginary y-axis too.
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