Fungrim home page

Fungrim entry: 54340e

sgn ⁣(z)=exp ⁣(iarg ⁣(z))\operatorname{sgn}\!\left(z\right) = \exp\!\left(i \arg\!\left(z\right)\right)
Assumptions:zC{0}z \in \mathbb{C} \setminus \left\{0\right\}
TeX:
\operatorname{sgn}\!\left(z\right) = \exp\!\left(i \arg\!\left(z\right)\right)

z \in \mathbb{C} \setminus \left\{0\right\}
Definitions:
Fungrim symbol Notation Short description
Signsgn ⁣(z)\operatorname{sgn}\!\left(z\right) Sign function
Expez{e}^{z} Exponential function
ConstIii Imaginary unit
Argarg ⁣(z)\arg\!\left(z\right) Complex argument
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("54340e"),
    Formula(Equal(Sign(z), Exp(Mul(ConstI, Arg(z))))),
    Variables(z),
    Assumptions(Element(z, SetMinus(CC, Set(0)))))

Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-09-15 11:00:55.020619 UTC