Fungrim entry: dcc1e5

\left|\log(z)\right| = \sqrt{\log^{2}\!\left(\left|z\right|\right) + {\left(\arg(z)\right)}^{2}}

Assumptions:

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
`Abs`	$\left\|z\right\|$	Absolute value
`Log`	$\log(z)$	Natural logarithm
`Sqrt`	$\sqrt{z}$	Principal square root
`Pow`	${a}^{b}$	Power
`Arg`	$\arg(z)$	Complex argument
`CC`	$\mathbb{C}$	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

Natural logarithm

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