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Homework Help: Order of poles

  1. Mar 27, 2006 #1
    I'm having trouble determining the order of the pole of

    [exp(iz) - 1]/((z^2) + 4) at z=2i

    I know I can't just expand the exponential as 1 + iz + [(iz)^2]/2 .......
    because this formula only works near the origin. Can I still use Taylor's theorem to find the expansion at z=2i (i.e does Taylor's theorem still work for complex variables?)
    thanks for your help.
     
  2. jcsd
  3. Mar 27, 2006 #2

    HallsofIvy

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    Science Advisor

    It's pretty obvious, isn't it, that f(z)(z-2i)= (eiz-1)/(z+2i) is analytic at z= 2i while f(z) itself is not. z= 2i is a pole of order 1.
     
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