By means of local Cauchy theorem find: $(i)\int_{|z|=1}\sqrt{9-z^2}dz; (ii) \int_{|z|=1}(z^2+2z)^{-1}dz; (iii)\int_{|z+i|=3/2}(z^4+z^2)^{-1}$
(i) Since $f$ is analytic for all $\mathbb{C}$ and $|z|=1$ is a closed path, one has to $\int_{|z|=1}\sqrt{9-z^2}dz=0$.
(ii) I know that P is analytic in all points except $z=0, z=-2$, so how can I use the theorem here? Also the path is not where $f$ is analytic, could you modify this?
(iii) I know that $f$ is analytic in all points except $z=0, z=\pm i$, and besides all these points are in $|z+i|=3/2$ minus $z=i$, how can I do in this case then? Thank you very much.