# Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.2 Trigonometric (Polar) Form of Complex Numbers - 8.2 Exercises - Page 371: 68c

For $z = a + bi$, if $(a, b)$ is in the Julia set, the conjugate of $z$, $\bar{z} = a - bi$, $(a, -b)$ is in the Julia set too.

#### Work Step by Step

For $z = a + bi$, if $(a, b)$ is in the Julia set, the absolute value of $z$ will not exceed 2 then. For the conjugate of $z$, $\bar{z} = a - bi$, since complex conjugates have the same absolute value (proved in 8.2 Ex. 64a), therefore, the absolute value of $\bar{z}$ will not exceed 2 also, and hence, $(a, -b)$ is in the Julia set too.

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