Fungrim home page

Fungrim entry: 57af50

−z=iz\sqrt{-z} = i \sqrt{z}
Assumptions:z∈[0,∞) or⁡ (z∈C and⁡ Im⁡ ⁣(z)<0)z \in \left[0, \infty\right) \,\mathbin{\operatorname{or}}\, \left(z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \operatorname{Im}\!\left(z\right) \lt 0\right)
TeX:
\sqrt{-z} = i \sqrt{z}

z \in \left[0, \infty\right) \,\mathbin{\operatorname{or}}\, \left(z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \operatorname{Im}\!\left(z\right) \lt 0\right)
Definitions:
Fungrim symbol Notation Short description
Sqrtz\sqrt{z} Principal square root
ConstIii Imaginary unit
ClosedOpenInterval[a,b)\left[a, b\right) Closed-open interval
Infinity∞\infty Positive infinity
CCC\mathbb{C} Complex numbers
ImIm⁡ ⁣(z)\operatorname{Im}\!\left(z\right) Imaginary part
Source code for this entry:
Entry(ID("57af50"),
    Formula(Equal(Sqrt(Neg(z)), Mul(ConstI, Sqrt(z)))),
    Variables(z),
    Assumptions(Or(Element(z, ClosedOpenInterval(0, Infinity)), And(Element(z, CC), Less(Im(z), 0)))))

Topics using this entry

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