\(\DeclarePairedDelimiterX{\Set}[2]{\{}{\}}{#1 \nonscript\;\delimsize\vert\nonscript\; #2}\) \( \DeclarePairedDelimiter{\set}{\{}{\}}\) \( \DeclarePairedDelimiter{\parens}{\left(}{\right)}\) \(\DeclarePairedDelimiterX{\innerproduct}[1]{\langle}{\rangle}{#1}\) \(\newcommand{\ip}[1]{\innerproduct{#1}}\) \(\newcommand{\bmat}[1]{\left[\hspace{2.0pt}\begin{matrix}#1\end{matrix}\hspace{2.0pt}\right]}\) \(\newcommand{\barray}[1]{\left[\hspace{2.0pt}\begin{matrix}#1\end{matrix}\hspace{2.0pt}\right]}\) \(\newcommand{\mat}[1]{\begin{matrix}#1\end{matrix}}\) \(\newcommand{\pmat}[1]{\begin{pmatrix}#1\end{pmatrix}}\) \(\newcommand{\mathword}[1]{\mathop{\textup{#1}}}\)
Needs:
Complex Numbers ›
Real Functions ›
Needed by:
Complex Analytic Functions ›
Complex Integrals ›
Complex Rational Functions ›
Holomorphic Functions ›
Links:
Sheet PDF ›
Graph PDF ›

Complex Functions

Why

We name functions whose domain is the complex numbers.

Definition

A complex function is a complex-valued function.1

Notation

Let $A$ be a set. Let $f: A \to \C $. $f$ is a complex function.

  1. Future editions will expand the discussion, and likely motivate the definition via the genetic approach. ↩︎
 Copyright © 2023 The Bourbaki Authors — All rights reserved — Version 13a6779cc — About — Show the old page view