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Homework Help: Power series, complex numbers

  1. Jan 3, 2010 #1
    We have already shown 1+ w+ w^2 =0

    If w is the complex number exp(2*Pi*i/3) , find the power series for;
    exp(z) +exp(w*z) + exp (z*w^2)

    We have already shown 1+ w+ w^2 =0
     
    Last edited: Jan 3, 2010
  2. jcsd
  3. Jan 3, 2010 #2

    Dick

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    If 1+w+w^2=0, can you tell me what are w^3, w^4, w^5 ...? Now do a power series expansion of the exponentials and combine like powers of z. Do you see a pattern?
     
  4. Jan 3, 2010 #3
    Thanks!

    So w^3=1
    w^4= w^1
    w^5=w^2 etc

    so
    exp(z) +exp(w*z) + exp (z*w^2)= 3 + 0 +0 + 3*z^3/3! + 0 + 0 +3*z^6/6! etc,

    But where do i go from here?
    Thankyou for your time
     
  5. Jan 3, 2010 #4

    Dick

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    You are done, aren't you? The problem asked for a simple form of the power series, and you just showed it to me.
     
  6. Jan 3, 2010 #5
    That is a valid point!

    Thanks dick
     
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