Definition:Complex Function

Definition

A complex function is a function whose domain and codomain are subsets of the set of complex numbers $\C$.

Independent Variable

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

Let $\map f z = w$.

Then $z$ is referred to as an independent variable (of $f$).

Dependent Variable

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

Let $\map f z = w$.

Then $w$ is referred to as the dependent variable (of $f$).

Also see

• Definition:Complex Transformation
• Definition:Multifunction

• Results about Complex Functions can be found here.

Sources

• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $2$: Functions, Limits and Continuity: Variables and Functions
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): function of a complex variable
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): complex function