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Complex Analysis - Series

  1. Feb 15, 2013 #1
    1. The problem statement, all variables and given/known data
    Assume that z_j is a sequence where j indexes from 1 to infinity are in the complex numbers such that the real part of z > 0. Is it true or false that if sum(z_j) and sum_((z_j)^2) both converge then sum(|z^j|^2) also converges?


    2. Relevant equations



    3. The attempt at a solution
    I tried breaking up z into real and imaginary parts and looking at what has to converge. For example, if z_j=x_j+iy_j, then the sum of x_j and sum of y_j both converge. Not really sure where else to go.
     
  2. jcsd
  3. Feb 15, 2013 #2

    HallsofIvy

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    What are the real and imaginary parts of [itex]z_j^2[/itex]?
     
  4. Feb 15, 2013 #3
    so the real part is x^2-y^2 and the imaginary part is 2xy
     
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