c
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
Also known as complex signum · sgn · signum of a complex number · signum
- Instance of
Overview
All data
17 statements · 12% with external sources · numbers in brackets are citations
- Image of function
- union class of object(s) of occurrence: complex unit circle, zero
- 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
- In defining formula
zsymbol represents: complex number\vert z \vertsymbol represents: magnitude of a complex number\{symbol represents: switch statement\operatorname{sgn} zsymbol represents: complex sign function\exp zsymbol represents: natural exponential function\mathrm{i}symbol represents: imaginary unit\operatorname{arg} zsymbol represents: argument