I am trying to calculate this Integral where Z is an element of the Complex number. I think I need to find the residue because there is a singularity (the center of the contour is actually the singularity $z = -1 + i$) So I Believe I should find the residue. Is this all correct? and if it is, how do I find the residue?
$c = -1 + i + e^{it} $
$ 0 < t \leq 2\pi$
$\int_c \frac1{(z^4 + 4)} dz$