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Math Help - complex numbers

  1. #1
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    complex numbers

    Verify that \sqrt{2}\mid{z}\mid is greater than or equal to \midRe(z) \mid + \midIm(z) \mid for any complex number z \in C
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  2. #2
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    This true for all real numbers: a^2+b^2\ge 2ab.
    So 2(a^2+b^2)=a^2+(a^2+b^2)+b^2\ge a^2 +2ab + b^2=(a+b)^2

    Let a=|\Re(z)|~\&~b=|\Im(z)| then does 2|z|^2\ge (a+b)^2 follow?

    Can you finish?
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