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    Proving complex variables

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    ** Please see the attached file for the full problem description **
    Please show all work in detail and how all steps.

    1. Prove that : ((2)^.5)*|z| ≥ |Re(z)| + Im(z)
    2. Suppose that either |z| =1 or |w|=1. Prove that |z-w| = |!-z(bar)*w|
    3. Prove that |z|=0 iff z=0

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    Solution Summary

    This solution provides a step-by-step explanation for how to prove the given complex variables.