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Fungrim entry: 60772e

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

z \in \mathbb{C} \setminus \left\{0\right\}
Definitions:
Fungrim symbol Notation Short description
Argarg(z)\arg(z) Complex argument
ConstIii Imaginary unit
Loglog(z)\log(z) Natural logarithm
Signsgn(z)\operatorname{sgn}(z) Sign function
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("60772e"),
    Formula(Equal(Arg(z), Neg(Mul(ConstI, Log(Sign(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.

2020-01-31 18:09:28.494564 UTC