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Thread: Prove |z1|=|z2|

  1. November 16th 2009, 06:28 PM #1
    arze
    arze is offline
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    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|.
    Thanks
    Attached Thumbnails Attached Thumbnails Prove |z1|=|z2|-graph.bmp  
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