Let $f: \Omega \subset \mathbb{C} \to \mathbb{C}$ be a [[Complex Numbers|complex]] function and $z\in \Omega$. We say that $f$ is complex differentiable at $z$ if and only if $\lim_{ h \to 0 } \frac{f(z+h)-f(z)}{h}$exists. We denote the limit $f'(z)$. **Terminology**: - We say that $f$ is **analytic** (or **holomorphic**) in a neighbourhood $U$ of $z$ if it is complex differentiable at every point in $U$. # Properties