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Math Help - Complex Analysis: Parallelogram Law

  1. #1
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    Complex Analysis: Parallelogram Law

    I need to prove the parallelogram law for complex numbers z and w: |z+w|^2+|z-w|^22|z|^2+2|w|^2. My approach follows:
    Proof: |z+w|^2+|z-w|^2=|z|^2+2|wz|+|w|^2+|z|^2-2|wz|+|w|^2=2|z|^2+2|w|^2

    Can I actually multiply |z+w| in this format? Thanks.
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  2. #2
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    Re: Complex Analysis: Parallelogram Law

    You can't do it like that because you're dealing with absolute value bars and not parentheses. Instead, start with
    |z+w|^2=(z+w)(\overline{z+w})
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  3. #3
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    Re: Complex Analysis: Parallelogram Law

    Thanks so much! I knew I had missed a property somewhere!
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