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Fungrim entry: 54340e

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

z \in \mathbb{C} \setminus \left\{0\right\}
Definitions:
Fungrim symbol Notation Short description
Signsgn(z)\operatorname{sgn}(z) Sign function
Expez{e}^{z} Exponential function
ConstIii Imaginary unit
Argarg(z)\arg(z) 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.

2019-12-30 15:00:46.909060 UTC