I got an annoying calculation question. The Res( \frac{z^a}{(z^2 + 1)^2},i ) = \frac{(1-a)exp(a
ipi/2)}{4i} is supposed to be this. Since i is a residue of order 2, there is a derivative involved. Now according to mathematica,
wolframalpha.com/input/?i=D%5Bx%5Ea%2F%28x+%2B+i%29%5E2%2Cx%5D , how does i^a disappear?