---
tag: 09E6T7VYAG
kind: concept
name: Complex differentiability
aliases: [complex-differentiable, complex-derivative]
msc: [30A99]
sources:
  - url: https://en.wikipedia.org/wiki/Holomorphic_function
    locator: Definition
---

## Summary

A complex function is complex differentiable at a point when its difference quotient has a limit as the complex increment goes to $0$. See the [[definition|0D1C9Y1EXA]].
The limit is the complex derivative.
A function that is complex differentiable at each point of an open set is holomorphic on that set.