Complex Function/Examples
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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 $\R$.