\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Prove that \(\arg(z_1 z_2) = \arg(z_1) + \arg(z_2) \pmod{2\pi}\) for any non-zero complex numbers \(z_1\) and \(z_2\).
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