## Trigonometry (11th Edition) Clone

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.
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.