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Orders of poles in the complex plane.

  1. Nov 28, 2009 #1
    1. The problem statement, all variables and given/known data
    For a function f(z)= [e^(2*pi*i*a*z)] / [1 + z^2] I need to find the order of the poles at i and -i.
    (I'm pretty sure these are the only poles.)

    2. Relevant equations



    3. The attempt at a solution
    I'm not totally clear on how I go about finding the orders. I have a vague idea: I can factorise the bottom line to get (z-i)(z+i) and I think this means that both poles are of order 1.
    But I want to try do the question by using the power series of the numerator and denominator, by comparing the number of "zero coefficients" in each power series.
    Anyone know how to do this method?
     
  2. jcsd
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