Fungrim entry: 99c0b3

\sqrt{z - c {z}^{2}} = \sqrt{z} \sqrt{1 - c z}

Assumptions:

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; c \in \left[0, \infty\right)

TeX:

\sqrt{z - c {z}^{2}} = \sqrt{z} \sqrt{1 - c z}

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; c \in \left[0, \infty\right)

Definitions:

Fungrim symbol	Notation	Short description
`Sqrt`	$\sqrt{z}$	Principal square root
`Pow`	${a}^{b}$	Power
`CC`	$\mathbb{C}$	Complex numbers
`ClosedOpenInterval`	$\left[a, b\right)$	Closed-open interval
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("99c0b3"),
    Formula(Equal(Sqrt(Sub(z, Mul(c, Pow(z, 2)))), Mul(Sqrt(z), Sqrt(Sub(1, Mul(c, z)))))),
    Variables(z, c),
    Assumptions(And(Element(z, CC), Element(c, ClosedOpenInterval(0, Infinity)))))

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