Fungrim entry: d8791e

\sqrt{{z}^{2}} = z

Assumptions:

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \arg\!\left(z\right) \in \left(\frac{-\pi}{2}, \frac{\pi}{2}\right]

TeX:

\sqrt{{z}^{2}} = z

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \arg\!\left(z\right) \in \left(\frac{-\pi}{2}, \frac{\pi}{2}\right]

Definitions:

Fungrim symbol	Notation	Short description
`Sqrt`	$\sqrt{z}$	Principal square root
`Pow`	${a}^{b}$	Power
`CC`	$\mathbb{C}$	Complex numbers
`Arg`	$\arg\!\left(z\right)$	Complex argument
`OpenClosedInterval`	$\left(a, b\right]$	Open-closed interval
`ConstPi`	$\pi$	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(ConstPi), 2), Div(ConstPi, 2))))))

Topics using this entry

Square roots

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