Fungrim home page

Fungrim entry: 12664e

∣z∣≤∣Re⁡ ⁣(z)∣+∣Im⁡ ⁣(z)∣\left|z\right| \le \left|\operatorname{Re}\!\left(z\right)\right| + \left|\operatorname{Im}\!\left(z\right)\right|
Assumptions:z∈Cz \in \mathbb{C}
TeX:
\left|z\right| \le \left|\operatorname{Re}\!\left(z\right)\right| + \left|\operatorname{Im}\!\left(z\right)\right|

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Abs∣z∣\left|z\right| Absolute value
ReRe⁡ ⁣(z)\operatorname{Re}\!\left(z\right) Real part
ImIm⁡ ⁣(z)\operatorname{Im}\!\left(z\right) Imaginary part
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("12664e"),
    Formula(LessEqual(Abs(z), Add(Abs(Re(z)), Abs(Im(z))))),
    Variables(z),
    Assumptions(Element(z, CC)))

Topics using this entry

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