Residue Theorem

${\oint }_{C}f(z)\mathrm{d}z=2\pi i\sum _{k=1}^n{\text{Res}}_{z=z_k}f$

• $C$ is a positively-oriented (counter-clockwise) simple closed contour
• $f$ is analytic on and inside $C$ except at finitely many singularities $z_1,\dots z_n$ inside $C$
• ${\text{Res}}_{z=z_k}f$ are the residues of $f$