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Fungrim entry: 099b19

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

z \in \mathbb{C} \setminus \left\{0\right\}
Definitions:
Fungrim symbol Notation Short description
ReRe⁡ ⁣(z)\operatorname{Re}\!\left(z\right) Real part
Loglog⁡ ⁣(z)\log\!\left(z\right) Natural logarithm
Abs∣z∣\left|z\right| Absolute value
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("099b19"),
    Formula(Equal(Re(Log(z)), Log(Abs(z)))),
    Variables(z),
    Assumptions(Element(z, SetMinus(CC, Set(0)))))

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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