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Fungrim entry: dcc1e5

log(z)=log2 ⁣(z)+(arg(z))2\left|\log(z)\right| = \sqrt{\log^{2}\!\left(\left|z\right|\right) + {\left(\arg(z)\right)}^{2}}
Assumptions:zC{0}z \in \mathbb{C} \setminus \left\{0\right\}
TeX:
\left|\log(z)\right| = \sqrt{\log^{2}\!\left(\left|z\right|\right) + {\left(\arg(z)\right)}^{2}}

z \in \mathbb{C} \setminus \left\{0\right\}
Definitions:
Fungrim symbol Notation Short description
Absz\left|z\right| Absolute value
Loglog(z)\log(z) Natural logarithm
Sqrtz\sqrt{z} Principal square root
Powab{a}^{b} Power
Argarg(z)\arg(z) Complex argument
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("dcc1e5"),
    Formula(Equal(Abs(Log(z)), Sqrt(Add(Pow(Log(Abs(z)), 2), Pow(Arg(z), 2))))),
    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