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Fungrim entry: 12664e

zRe ⁣(z)+Im ⁣(z)\left|z\right| \le \left|\operatorname{Re}\!\left(z\right)\right| + \left|\operatorname{Im}\!\left(z\right)\right|
Assumptions:zCz \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
Absz\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)))

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2019-09-15 14:14:26.267625 UTC