06 - Cauchy or Cauchy-Goursat Theorem

Cauchy or Cauchy-Goursat Theorem

Let $U\subset \mathbb{C}$ be a domain
Let $\gamma$ be a closed curve such that $\gamma$ and all bounded components of $\mathbb{C}\setminus {\gamma }^{\ast }$ are inside $U$

Let $f$ be a function holomorphic in $U$ then

$${\int }_{\gamma }f(z)dz=0$$

Proof - Lecture Notes

Refer to lecture notes (page 48)