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Complex line integral

  1. Sep 6, 2011 #1
    I can't find the value, for natural number [itex] n = 1, 2, 3, ... [/itex]
    [itex] I = \int\limits_{C}\dfrac{e^{iz}}{z^n} dz [/itex]

    find the value. where [itex]z(t) =e^{it}[/itex] , [itex]0\leq t \leq 2\Pi[/itex]
  2. jcsd
  3. Sep 6, 2011 #2


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    Science Advisor

    Have you considered applying Cauchy's integral formula,
    [tex]f^{(n)}(z)= \frac{1}{2\pi i}\oint_C \frac{f(z)}{(z- a)^{n+1}} dz[/tex]
    where C is any closed path containing a?
    What is f(z)? What is a?
  4. Sep 6, 2011 #3
    I didn't apply, but in the question f(z) is not given, and also a.
    can we choose as f(z)=e^{iz} and a=0 ?
  5. Sep 6, 2011 #4
    sorry for mistake
    f(z)=e^{iz} --------> f(z)=e^{it} .
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