Question 2

Question

Holomorphic functions and their properties.

Answer

A holomorphic is a function $f:D\to \mathbb{C}$ with a domain $D$.

It is holomorphic at $z_0$ if $f$ is differentiable in an open disk (entered at $z_0$).

Complex differentiable

It is differentiable if the following limit exists:
${\lim }_{\Delta z\to \infty }\frac{f(z+\Delta z)-f(z)}{\Delta z}$