# complex contour line Integral

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?

$$c = -1 + i + e^{it}$$

$$0 < t \leq 2\pi$$

$$\int_c \frac1{(z^4 + 4)} dz$$

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Recall that if $z_1$ is a simple singularity of $f(z)$
$$\operatorname{Res}_{z=z_1} f(z)= \lim_{z \to z_1} (z-z_1)f(z)$$