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Math Help - Complex numbers lying on the same side of a straight line passing through the origin.

  1. #1
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    Complex numbers lying on the same side of a straight line passing through the origin.

    I need help with this problem:

    Let Zk (k = 1, ... , n) be complex numbers lying on the same side of a straight line passing through the origin. Show that

    z1 + z2 + ... + zn ≠ 0 and
    1/z1 + 1/z2 + ... + 1/zn ≠ 0
    Last edited by mr fantastic; March 9th 2011 at 07:59 PM. Reason: Re-titled.
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  2. #2
    Senior Member Tinyboss's Avatar
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    Multiply everything by some unimodular complex number (i.e. rotate everything) so that the line becomes the real axis. The result should be easy to show in that setting--then divide by the same number to get the result you want.
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