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Homework Help: Solving a complex equation with roots of unity

  1. Jan 12, 2010 #1
    1. The problem statement, all variables and given/known data

    z is a complex number.

    Find all the solutions of

    (z+1)^5 = z^5

    3. The attempt at a solution

    Of course one could expand (z+1)^5, but I remeber our professor solving this with roots of unity. Can anyone help?
     
  2. jcsd
  3. Jan 12, 2010 #2
    Ah, embarissing.

    1=(z+1)^5/z^5
    =((z+1)/z)^5

    and then just using the roots of unity to find z= 1/(1-w) , w=exp(i*2k*pi/5), k=1,2,3,4.
     
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