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

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