Fungrim home page

Fungrim entry: c43533

log⁡(z)=log⁡ ⁣(∣z∣)+arg⁡(z)i\log(z) = \log\!\left(\left|z\right|\right) + \arg(z) i
Assumptions:z∈C∖{0}z \in \mathbb{C} \setminus \left\{0\right\}
TeX:
\log(z) = \log\!\left(\left|z\right|\right) + \arg(z) i

z \in \mathbb{C} \setminus \left\{0\right\}
Definitions:
Fungrim symbol Notation Short description
Loglog⁡(z)\log(z) Natural logarithm
Abs∣z∣\left|z\right| Absolute value
Argarg⁡(z)\arg(z) Complex argument
ConstIii Imaginary unit
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("c43533"),
    Formula(Equal(Log(z), Add(Log(Abs(z)), Mul(Arg(z), ConstI)))),
    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.

2021-03-15 19:12:00.328586 UTC