Let . Find
in terms of , where is the circle oriented in the counterclockwise
direction.
I tried to express as . Then how should I proceed on? Any idea/suggestion is welcomed!
First, we need to check that there are not any singularities. The only place where there may be a singularity is where . But this is not possible since on the contour , for that denominator to be 0, , but we know . Now since is the unit circle oriented in the counterclockwise direction centred at the origin, we can parameterise it as with . Notice that and the integral becomes
Now let and note that and giving