Each of the following integrals is zero. Give a brief reason for each example.
Not sure about But I think it is the circle centered at with radius 2.
(i)
Not sure how to start this.
(ii)
Here,Cauchy's theorem can be applied. Since is differentiable in \{-2} and is a closed contour in \{-2} which does not wind round any points outside \{-2}, by Cauchy's Theorem.
(iii)
I have tried finding where is differentiable in order to use Cauchy's theorem as in (ii) but haven't really managed to do that.