07 - Homotopy Cauchy's Theorem

Homotopy Cauchy's Theorem / Deformation Theorem

Let $U$ be a domain in $\mathbb{C}$
Suppose that ${\gamma }_1$ and ${\gamma }_2$ are two paths in $U$ and are homotopic in $U$

Let $f:U\to \mathbb{C}$ be a holomorphic function then

$${\int }_{{\gamma }_1}f(z)dz={\int }_{{\gamma }_2}f(z)dz$$

Proof - Non-Examinable