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: 64d

Answer

The graph of the Julia set must be symmetric with respect to the $x-axis$.

Work Step by Step

For $z = a + bi$, the conjugate of $z$ is $\bar{z} = a - bi$ Since $z$ and $\bar{z}$ are symmetric with respect to the $x-axis$, and both $z$ and $\bar{z}$ are in the Julia set as well (proved in 8.2 Ex. 64c), therefore, the graph of the Julia set must be symmetric with respect to the $x-axis$ too.
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