# Definition:Primitive (Calculus)/Complex

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## Contents

## Definition

Let $F: D \to \C$ be a complex function which is complex-differentiable on a connected domain $D$.

Let $f: D \to \C$ be a continuous complex function.

Let:

- $\forall z \in D: \map {F'} z = \map f z$

where $F'$ denotes the derivative of $F$ with respect to $z$.

Then $F$ is **a primitive of $f$**, and is denoted:

- $\displaystyle F = \int \map f z \rd z$

## Also known as

A **primitive** is also known as an **antiderivative**.

The term **indefinite integral** is also popular.

## Also see

- Results about
**complex integral calculus**can be found here.

## Sources

- 2001: Christian Berg:
*Kompleks funktionsteori*: $\S 2.3$