Complex Function/Examples/Principal Argument

Example of Complex Function

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 $\R$.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): complex function (function of a complex variable)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): complex function (function of a complex variable)