1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

    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!
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook