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Math Help - Complex numbers and triangles?

  1. #1
    Super Member fardeen_gen's Avatar
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    Jun 2008
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    Complex numbers and triangles?

    If z_1,z_2,z_3 be the complex numbers represented by the vertices A, B, C of a triangle \mbox{ABC} in anticlockwise order, show that:

    \left|\sum \frac{z_2 - z_3}{z_1}|z_1|^2\right|\cos A - 2R[(z_1 - z_2)(\bar{z_1} - \bar{z_2})]\sin A = 0
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  2. #2
    Senior Member
    Joined
    Apr 2009
    From
    Atlanta, GA
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    408

    Clarity?

    Just to clarify...

    R[a+bi]=a

    \sum \frac{z_2 - z_3}{z_1}|z_1|^2= \frac{z_2 - z_3}{z_1}|z_1|^2+\frac{z_3 - z_1}{z_2}|z_2|^2+\frac{z_1 - z_2}{z_3}|z_3|^2
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