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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 \(z\).