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.