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Algebra Level 4

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

Does the above property hold for each complex number zz?

Clarifications:

  • Arg(z)\text{Arg}(z) is the principal argument of complex number zz, with a range of (π,π] (-\pi, \pi ] .

  • zˉ\bar z is the complex conjugate of complex number zz.

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