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Math Help - Complex numbers inequality

  1. #1
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    Complex numbers inequality

    prove that

    |z_1|^2 + |z_2|^2 + |z_1 + z_2|^2  \ge \frac{ 2(|a\cdot z_1 + b\cdot z_2|^2)}{(a^2 + b^2)}

    z_1 and z_2 are complex numbers and a and b are non zero real numbers
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  2. #2
    Senior Member JaneBennet's Avatar
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    Dec 2007
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    Try z_1=i,\ z_2=-i,\ a=1,\ b=-1.
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