Cauchy's residue theorem

In complex analysis, Cauchy’s residue theorem states that for a function $f(z)$ that is analytic on and inside a simple closed curve $C$ except possibly at finitely many points $z_1,\cdots ,z_n$ inside $C$, then:

$${\oint }_{C}f(z)dz=2\pi i\sum _{j=1}^n\text{Res}(f(z),z_i)$$

The residue theorem is functionally a superset of the Cauchy-Goursat theorem and Cauchy’s integral formula.