Not a simply connected contour

[oddiseas]

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 each other. 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

 

[Billy Bob]

"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.