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Fungrim entry: d8791e

z2=z\sqrt{{z}^{2}} = z
Assumptions:zCandarg(z)(π2,π2]z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \arg(z) \in \left(\frac{-\pi}{2}, \frac{\pi}{2}\right]
TeX:
\sqrt{{z}^{2}} = z

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \arg(z) \in \left(\frac{-\pi}{2}, \frac{\pi}{2}\right]
Definitions:
Fungrim symbol Notation Short description
Sqrtz\sqrt{z} Principal square root
Powab{a}^{b} Power
CCC\mathbb{C} Complex numbers
Argarg(z)\arg(z) Complex argument
OpenClosedInterval(a,b]\left(a, b\right] Open-closed interval
Piπ\pi The constant pi (3.14...)
Source code for this entry:
Entry(ID("d8791e"),
    Formula(Equal(Sqrt(Pow(z, 2)), z)),
    Variables(z),
    Assumptions(And(Element(z, CC), Element(Arg(z), OpenClosedInterval(Div(Neg(Pi), 2), Div(Pi, 2))))))

Topics using this entry

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

2019-11-19 15:10:20.037976 UTC