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system of equations-complex number

Discussion in 'Mathematics' started by John1357, Oct 8, 2018.

  1. John1357

    John1357 Guest

    I have a task: Prove that if for each complex number u,w,z we have:

    $uwz=1$ and $u+w+z=u^{-1}+w^{-1}+z^{-1}$

    then at least one of them is equal 1.

    I tried substituting $u=(uw)^{-1}$ to the second equality and prove that by denying, but I can't solve it.

    Thanks in advance.

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