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Math Help - Find the complex numbers

  1. #1
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    Find the complex numbers

    Find the complex numbers z_1, z_2, z_3, so that |z_1|=|z_2|=|z_3|=1 and z_1+z_2+z_3=z_1\cdot z_2\cdot z_3=1.

    Comment>
    I know that z_1, z_2, z_3 are on circle with r=1.
    And know x_1+x_2+x_3=1.

    How to combine it for product?

    Thank you.
    Last edited by feferon11; October 2nd 2013 at 01:27 PM.
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  2. #2
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    Re: Find the complex numbers

    Since arguments of complex numbers are added under multiplication of these numbers, z_1z_2z_3=1 means that \arg z_1+\arg z_2+\arg z_3 is a multiple of 2\pi.
    Thanks from topsquark and feferon11
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  3. #3
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    Re: Find the complex numbers

    Quote Originally Posted by feferon11 View Post
    Find the complex numbers z_1, z_2, z_3, so that |z_1|=|z_2|=|z_3|=1 and z_1+z_2+z_3=z_1\cdot z_2\cdot z_3=1.

    Comment>
    I know that z_1, z_2, z_3 are on circle with r=1.
    And know x_1+x_2+x_3=1.

    How to combine it for product?

    Thank you.
    Find the complex numbers-untitled2.gif
    Thanks from topsquark and feferon11
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