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Homework Help: Complex number and power series

  1. May 24, 2010 #1
    1. The problem statement, all variables and given/known data

    Let ω be the complex number e^(2πi/3), Find the power series for e^z + e^(ωz) + e^((ω^2) z).




    2. Relevant equations



    3. The attempt at a solution
    I can show that 1+w+w^2=0, dunno if it would help. Could anyone plz give me some hints? Any input is appreciated!
     
  2. jcsd
  3. May 24, 2010 #2

    Dick

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    Write out the three individual power series and sum them. Collect like powers of z. Use your equation for w to try and simplify the coefficients.
     
  4. May 24, 2010 #3
    I can write it as the sum of (z^n)*(1+w^n+w^2n)/n!, n from 0 to infinity. But I'm still not sure how to simplify 1+w^n+w^2n from 1+w+w^2=0. Could you explain it in a bit more details? Thanks a lot!
     
  5. May 24, 2010 #4

    Dick

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    Look at the n=0,1,2,3 cases. Hint, what's w^3? Once you've got those you should find it pretty easy to generalize.
     
  6. May 24, 2010 #5
    thanks, I got it!
     
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