Let $\displaystyle f(z) = \frac{e^{i z}}{(1+z^2)^2}$

Find the singularities and classify them. Find the residue when z = i.

Singularities found to be i and -i, both poles of order 2. So i figure ill need the taylor expansion at some point.

Is there a set way to calculate residues? The question i did before this involved differentiating the denominator but that wont work here since there will still be a zero on the bottom line. So how to i find residues if they are of order 2?