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The signum function is the real valued function defined for real as follows
For all real we have . Similarly, . If then also . The second property implies that for real non-zero we have .
For a complex argument it is defined by
where denotes the magnitude (absolute value) of . In other words, the signum function project a non-zero complex number to the unit circle .
We have , where is the complex conjugate of .
Cite this web-page as:Štefan Porubský: Signum Function.