(adsbygoogle = window.adsbygoogle || []).push({}); 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

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# Homework Help: Another complex integral, TOUGH!

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