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Mathematical Analysis
Special Functions

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### Signum Function

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*.

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