Answer
The complex conjugates of $z$ have the same absolute value.
Work Step by Step
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.
