Fungrim entry: 792c76

\left|\log(z)\right| \le \left|\log\!\left(\left|z\right|\right)\right| + \pi

Assumptions:

z \in \mathbb{C} \setminus \left\{0\right\}

TeX:

\left|\log(z)\right| \le \left|\log\!\left(\left|z\right|\right)\right| + \pi

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
`Pi`	$\pi$	The constant pi (3.14...)
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("792c76"),
    Formula(LessEqual(Abs(Log(z)), Add(Abs(Log(Abs(z))), Pi))),
    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