Complex-Valued Function

complex-analysis

Definition

Complex-Valued Function

A complex-valued function is a function whose codomain is the set of complex numbers $\mathbb{C}$.

Formally, if $X$ is a set, then

$$f:X\to \mathbb{C}.$$

For each $x\in X$, the value $f(x)$ has the form

$$f(x)=a+bi,$$

where $a,b\in \mathbb{R}$ and $i^2=-1$.