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Thread: Prove |z1|=|z2|

  1. #1
    Senior Member
    Jul 2009

    Prove |z1|=|z2|

    The points A and B represent the complex numbers z_1 and z_2 respectively on an Argand diagram, where 0<argz_2<argz_1<\frac{\pi}{2}.
    Give geometrical constructions to find the points C and D representing z_1+z_2 and z_1-z_2 respectively.
    Given that arg(z_1-z_2)-arg(z_1+z_2)=\frac{\pi}{2}, pprove that |z_1|=|z_2|.

    I attached the diagram. What I need help with is proving that |z_1|=|z_2|.
    Attached Thumbnails Attached Thumbnails Prove |z1|=|z2|-graph.bmp  
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