Definition:Complex-Valued Function

Definition

Let $f: S \to T$ be a function.

Let $S_1 \subseteq S$ such that $f \left({S_1}\right) \subseteq \C$.

Then $f$ is defined as complex-valued on $S_1$.

That is, $f$ is defined as complex-valued on $S_1$ if the image of $S_1$ under $f$ lies entirely within the set of complex numbers $\C$.

A complex-valued function is a function $f: S \to \C$ whose codomain is the set of complex numbers $\C$.

That is $f$ is complex-valued iff it is complex-valued over its entire domain.

Also see

• Definition:Real-Valued Function: Note that as $\R \subseteq \C$, it is technically correct to refer to a real-valued function as complex-valued.

• Results about complex-valued functions can be found here.

Sources

There are no source works cited for this page. Source citations are highly desirable, and mandatory for all definition pages. Definition pages whose content is wholly or partly unsourced are in danger of having such content deleted. To discuss this page in more detail, feel free to use the talk page.