Fungrim entry: c58f46

\sqrt{\overline{z}} = \overline{\sqrt{z}}

Assumptions:

z \in \mathbb{C} \setminus \left(-\infty, 0\right)

TeX:

\sqrt{\overline{z}} = \overline{\sqrt{z}}

z \in \mathbb{C} \setminus \left(-\infty, 0\right)

Definitions:

Fungrim symbol	Notation	Short description
`Sqrt`	$\sqrt{z}$	Principal square root
`Conjugate`	$\overline{z}$	Complex conjugate
`CC`	$\mathbb{C}$	Complex numbers
`OpenInterval`	$\left(a, b\right)$	Open interval
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("c58f46"),
    Formula(Equal(Sqrt(Conjugate(z)), Conjugate(Sqrt(z)))),
    Variables(z),
    Assumptions(Element(z, SetMinus(CC, OpenInterval(Neg(Infinity), 0)))))

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