Complex Function/Examples

Examples of Complex Functions

Square Function

Let $f: \C \to \C$ be the function defined as:

$\forall z \in \C: \map f z = z^2$

This is a complex function.

Imaginary Part

Let $f: \C \to \C$ be the function defined as:

$\forall z \in \C: \map f z = \map \Im z$

where $\map \Im z$ denotes the imaginary part of $z$.

$f$ is a complex function whose image is the set of real numbers $\R$.

Principal Argument

Let $f: \C \to \C$ be the function defined as:

$\forall z \in \C: \map f z = \Arg z$

where $\Arg z$ denotes the principal argument of $z$.

$f$ is a complex function whose image is the set of real numbers $\R$.