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Homework Help: Another complex integral, TOUGH!

  1. Jun 22, 2007 #1

    malawi_glenn

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    1. The problem statement, all variables and given/known data
    Evaluate:

    [tex] \int _{c} \dfrac{1- Log z}{z^{2}} dz [/tex]

    where C is the curve:

    [tex] C : z(t) = 2 + e^{it} ; - \pi / 2 \leq t \leq \pi / 2 [/tex]


    2. Relevant equations
    I know the independance of path in a domain where f(z) is analytical, but I tried the standard parametrization just to beging with someting.


    3. The attempt at a solution

    [tex] z^{2} = 4 + 4e^{it} + e^{2it} [/tex]

    [tex] Log(2 + e^{it} ) = \frac{1}{2} \ln (5 + \cos t) +it [/tex]

    [tex] dz = ie^{it} dt [/tex]

    [tex] i \int _{- \pi / 2} ^{\pi / 2} \dfrac{1 -\frac{1}{2} \ln (5 + \cos t) -it }{4 + 4e^{it} + e^{2it}}e^{it} dt [/tex]

    lol iam lost
     
  2. jcsd
  3. Jun 22, 2007 #2

    malawi_glenn

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    do you think I shall use independance of path?
     
  4. Jun 22, 2007 #3

    malawi_glenn

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    never mind, I solved it.
     
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