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Complex Analysis (Practice Exam)

  1. Apr 27, 2010 #1
    1. The problem statement, all variables and given/known data

    This question is in my exam review problem from my complex analysis class.
    Compute f(100)(0)/100!, where f(z) = 1/(1+i-sqrt(2)z).

    (f(100)(0) means the 100th derivative of f evaluated at 0.)
    2. Relevant equations

    Cauchy's integral formula might be helpful.

    The answer to this question is -1/(1+i).

    3. The attempt at a solution

    I thought about using Cauchy's integral formula, but it seems like I need to rewrite f(z) so that I have singularity at 0... or maybe I'm completely missing out.

    Thanks!
     
  2. jcsd
  3. Apr 27, 2010 #2
    Have you tried writing the function as it's series representation about 0? Then the calculation you are looking for would be the coefficient in front of the z^100 term.
     
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