Fungrim entry: 08d275

\mathop{\operatorname{zeros}\,}\limits_{z \in \mathbb{C}} \left[{z}^{2} - c\right] = \left\{\sqrt{c}, -\sqrt{c}\right\}

Assumptions:

c \in \mathbb{C}

TeX:

\mathop{\operatorname{zeros}\,}\limits_{z \in \mathbb{C}} \left[{z}^{2} - c\right] = \left\{\sqrt{c}, -\sqrt{c}\right\}

c \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`Zeros`	$\mathop{\operatorname{zeros}\,}\limits_{x \in S} f(x)$	Zeros (roots) of function
`Pow`	${a}^{b}$	Power
`CC`	$\mathbb{C}$	Complex numbers
`Sqrt`	$\sqrt{z}$	Principal square root

Source code for this entry:

Entry(ID("08d275"),
    Formula(Equal(Zeros(Sub(Pow(z, 2), c), ForElement(z, CC)), Set(Sqrt(c), Neg(Sqrt(c))))),
    Variables(c),
    Assumptions(Element(c, CC)))

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.

2021-03-15 19:12:00.328586 UTC