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Math Help - argument of a complex number

  1. #1
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    argument of a complex number

    If |z1 + z2| = |z1 - z2|, prove that the difference between the arguments (of z1 and z2) is pi/2.

    I'd be grateful for any help or pointers in trying to prove this please. Thanks.
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  2. #2
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    write them down as exponential funcitons: z1=r1*exp(i*phi1)
    calculate the |z1+z2| by multiplying by the same with -i instead of i
    r1 and r2 all fall out
    it stays exp(i*(phi1-phi2)) = - exp(-i*(phi1-phi2))
    divide by exp(-i*(phi1-phi2))
    now it's exp(i*2*(phi1-phi2)) = -1
    so phi1-phi2 must be pi/2 because exp(i*2*pi/2)=exp(i*pi)=-1
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