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Fungrim entry: c43533

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

z \in \mathbb{C} \setminus \left\{0\right\}
Definitions:
Fungrim symbol Notation Short description
Loglog⁡ ⁣(z)\log\!\left(z\right) Natural logarithm
Abs∣z∣\left|z\right| Absolute value
Argarg⁡ ⁣(z)\arg\!\left(z\right) 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.

2019-06-18 07:49:59.356594 UTC