Thread: Complex Variables: Contour Integral

1. Complex 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

2. Re: 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.

3. Re: Complex Variables: Contour Integral

Yes but I'm not sure how to parametrize the curves in order to solve it by integrating directly

4. Re: Complex Variables: Contour Integral

First of all draw a picture to see what $C$ looks like, it is crucial when doing this kind of integrals.