Let C=C1UC2 where C1 and C2 are respectively the smaller arcs of the circles |z-i|=1 and |z-1|=1 joining the points z1=0+0i and z2=1+i

By using the definition of a contour integral evaluate

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- Apr 3rd 2013, 05:38 PMcheesecake91Complex Variables: Contour Integral
Let C=C1UC2 where C1 and C2 are respectively the smaller arcs of the circles |z-i|=1 and |z-1|=1 joining the points z1=0+0i and z2=1+i

By using the definition of a contour integral evaluate

Attachment 27790 - Apr 3rd 2013, 05:51 PMSworDRe: Complex Variables: Contour Integral
This is a closed path isn't it? Unless I misunderstood the question and it isn't, the integral will be 0 by Cauchy's integral theorem.

- Apr 3rd 2013, 07:32 PMcheesecake91Re: Complex Variables: Contour Integral
Yes but I'm not sure how to parametrize the curves in order to solve it by integrating directly

- Apr 4th 2013, 01:57 AMRuunRe: Complex Variables: Contour Integral
First of all draw a picture to see what $\displaystyle C$ looks like, it is crucial when doing this kind of integrals.