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Algebra Level 4

$\large \text{Arg} (\bar{z}) =- \text{Arg}(z)$

Does the above property hold for each complex number $z$ ?

Clarifications:

$\text{Arg}(z)$ is the principal argument of complex number $z$ , with a range of $(-\pi, \pi ]$ .
$\bar z$ is the complex conjugate of complex number $z$ .