# Definition:Modulus of Complex-Valued Function

Let $f: S \to \C$ be a complex-valued function.
Then the (complex) modulus of $f$ is written $\left|{f}\right|: S \to \R$ and is the real-valued function defined as:
$\forall z \in S: \left|{f}\right| \left({z}\right) = \left|{f \left({z}\right)}\right|$.