# Complex line integral over x + y = 1

1. Apr 16, 2013

### Verdict

1. The problem statement, all variables and given/known data

2. Relevant equations
I can't think of many to begin with. I've mainly been dealing with the simple forms of Cauchy's theorem so far, such as the Cauchy-Goursat theorem, and also Cauchy's integral formulas. However, these don't seem to have any direct implications here.

3. The attempt at a solution
Alright, so I first used partial fraction expansion to rewrite the integral as
i/4 [integral over dz/(z+2i) - integral over dz/(z-2i)]
However, then I have to parametrize the curve. Now, I tried using z = x + iy, and then parametrising the curve so that x = 1 - y, but that doesn't really seem to be going anywhere. I also don't see how that relates to the hint, nor do I see a way to start solving the problem from the hint.

Could someone maybe provide me with a tip as to what I should be doing?