complex sign function
complex-to-complex function which takes a number and returns its "direction" in the form of a number on the complex unit circle, or zero
Facts
9 properties- Instance of
- sign function, complex function[2]
- Defining formula
- \operatorname{sgn} z = \begin{cases} \frac{z}{\vert z \vert} & z \ne 0 \\ 0 & z = 0 \end{cases}, \operatorname{sgn} z = \exp(\mathrm{i} \operatorname{arg} z), z \neq 0[10][11]
- Definition domain
- set of complex numbers[4]
- Described by source
- ISO 80000-2:2019 Quantities and units — Part 2: Mathematics[3]
- Different from
- real sign function, argument, csgn complex sign function, sign function[5][6][7][8]
- Imported from
- wholeness_audit_2026-05-02
- In defining formula
- z, \vert z \vert, \{, \operatorname{sgn} z, \exp z, \mathrm{i}, \operatorname{arg} z[13][14][15][16][17][18][19]
- Maintained by WikiProject
- WikiProject Mathematics[12]
🏷️ Also known as
en complex signum
en complex sign function
en signum of a complex number
en signum
en sgn
cs komplexní funkce signum
cs komplexní signum
de Vorzeichenfunktion einer komplexen Zahl
de Signumfunktion einer komplexen Zahl
de Signumfunktion
de Signum einer komplexen Zahl
de komplexe Vorzeichenfunktion
de komplexe Signumfunktion
es signo de un número complejo
fr signum d'un nombre complexe
he פונקציית הסימן המרוכבת
ru комплексная функция знака
ru комплекснозначная функция знака
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Summary
complex sign function is a sign function[1].