Given the function $$F(z)= \frac{z^2}{((z^2)+1)^2(z^2+2z+2)},$$ determine its singularities and then calculate the corresponding residues.
Finding the zeros i got $\pm i$ and $-1\pm i$ for pole with order $2$ and simple pole, respectively. Calculating the residue for the simple pole and pole with order $2$, I got $\pm \frac{2i}{2i+1}$, and $±\frac{4}{4i-3}$ respectively.
I have a feeling my work is not correct, so any help or correction would be appreciated
Also would it be a removable singularity at $z=0$?