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Math Help - complex numbers argand diagram

  1. #1
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    complex numbers argand diagram

    If, with an Argand diagram with origin O, the point P represents z and Q represents 1/(conjugate of z), prove that O, P and Q are collinear and find the ratio OP:OQ in terms of |z|.

    ive tried letting z = x + iy so that P = (x + iy) but i havnt got far totally stuck
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  2. #2
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    Try letting z=re^{i\theta}.
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  3. #3
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    ok that worked really well i used z = r cis (theta) and i proved the angle the complex numbers make is the same so therefore collinear, but i do not understand how to find the ratio OP:OQ in terms of |z|
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  4. #4
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    |z|=r. Does that help?
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