Fungrim home page

Fungrim entry: caf706

sgn ⁣(ez)=exp ⁣(Im(z)i)\operatorname{sgn}\!\left({e}^{z}\right) = \exp\!\left(\operatorname{Im}(z) i\right)
Assumptions:zCz \in \mathbb{C}
TeX:
\operatorname{sgn}\!\left({e}^{z}\right) = \exp\!\left(\operatorname{Im}(z) i\right)

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Signsgn(z)\operatorname{sgn}(z) Sign function
Expez{e}^{z} Exponential function
ImIm(z)\operatorname{Im}(z) Imaginary part
ConstIii Imaginary unit
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("caf706"),
    Formula(Equal(Sign(Exp(z)), Exp(Mul(Im(z), ConstI)))),
    Variables(z),
    Assumptions(Element(z, CC)))

Topics using this entry

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

2019-10-05 13:11:19.856591 UTC