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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}(z) < 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}(z) < 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}(z) 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.

2021-03-15 19:12:00.328586 UTC