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Fungrim entry: dcc1e5

log ⁣(z)=(log ⁣(z))2+(arg ⁣(z))2\left|\log\!\left(z\right)\right| = \sqrt{{\left(\log\!\left(\left|z\right|\right)\right)}^{2} + {\left(\arg\!\left(z\right)\right)}^{2}}
Assumptions:zC{0}z \in \mathbb{C} \setminus \left\{0\right\}
TeX:
\left|\log\!\left(z\right)\right| = \sqrt{{\left(\log\!\left(\left|z\right|\right)\right)}^{2} + {\left(\arg\!\left(z\right)\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\!\left(z\right) Natural logarithm
Sqrtz\sqrt{z} Principal square root
Powab{a}^{b} Power
Argarg ⁣(z)\arg\!\left(z\right) 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.

2019-09-19 20:12:49.583742 UTC