Cauchy's integral theorem

In mathematics, the Cauchy integral theorem (also known as the Cauchy–Goursat theorem) in complex analysis, named after Augustin-Louis Cauchy (and Édouard Goursat), is an important statement about line integrals for holomorphic functions in the complex plane. Essentially, it says that if f ( z ) {\displaystyle f(z)} is holomorphic in a simply connected domain ⁠ Ω {\displaystyle \Omega } ⁠, then for any simple closed contour C {\displaystyle C} in ⁠ Ω {\displaystyle \Omega } ⁠, that contour integral is zero.

Source: Wikipedia — Cauchy's integral theorem (CC BY-SA 4.0)