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Fungrim entry: 12664e

zRe(z)+Im(z)\left|z\right| \le \left|\operatorname{Re}(z)\right| + \left|\operatorname{Im}(z)\right|
Assumptions:zCz \in \mathbb{C}
TeX:
\left|z\right| \le \left|\operatorname{Re}(z)\right| + \left|\operatorname{Im}(z)\right|

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Absz\left|z\right| Absolute value
ReRe(z)\operatorname{Re}(z) Real part
ImIm(z)\operatorname{Im}(z) 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)))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-12-30 15:00:46.909060 UTC