# Using residue theorem separately for real and imaginary parts

I'm trying to calculate an integral with respect to a complex value. I just want to know if I can estimate the integral using the residue theorem separately for the real and imaginary parts of the mentioned value or I cannot at all use this method here.

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Identify the poles within the given curve and the corresponding residues (=coefficients of $(z-a_0)^{-1}$ in the Laurent series). – Berci Mar 19 '13 at 12:45
$$\frac{1}{2 \pi i} \oint_C \frac{\pi dz}{z - 0.5 i} = \pi$$ – muzzlator Mar 19 '13 at 13:24