Not a simply connected contour

  • Thread starter oddiseas
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  • #1
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Homework Statement



I have a contour in the complex plane it is not simply connected, because it looks like two figure eights that overlap and intersect eachother. Now how do i evaluate an integral for such a contour?

Homework Equations



The question asks to evalute the contour shown for ∫dz/z-1.
But the contour is not simply connected and we are not given a function for the contour only a picture. In addition the discontinuity at z=1 is inside the contour. So how can i evaluate it?

Is this a trick question or something?
I thought we could only evaluate integrals when the contour is simply connected and we use a contour that does not contain the discontinuity?



The Attempt at a Solution

 

Answers and Replies

  • #2
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"Simply connected" would describe the domain, not the contour. I bet you mean the contour is not simple. You have to figure out the winding number of the contour around the point z=1. How many times does the contour wrap around z=1. Then you probably have a formula in your notes or book involving winding number.
 

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