## Trigonometry (11th Edition) Clone

The complex conjugates of $z$ have the same absolute value.
For $z = a + bi$, the absolute value of $z$ is $\sqrt{a^2 + b^2}$, while, for the conjugate of $z$, $\bar{z} = a - bi$, the absolute value of $\bar{z}$ is $\sqrt{a^2 + (-b)^2}$, which is also equal to $\sqrt{a^2 + b^2}$ Therefore, the complex conjugates of $z$ have the same absolute value.