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Fungrim entry: 08bd37

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

z \in \left(-\infty, 0\right] \,\mathbin{\operatorname{or}}\, \left(z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \operatorname{Im}\!\left(z\right) \gt 0\right)
Definitions:
Fungrim symbol Notation Short description
Sqrtz\sqrt{z} Principal square root
ConstIii Imaginary unit
OpenClosedInterval(a,b]\left(a, b\right] Open-closed 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("08bd37"),
    Formula(Equal(Sqrt(Neg(z)), Mul(Neg(ConstI), Sqrt(z)))),
    Variables(z),
    Assumptions(Or(Element(z, OpenClosedInterval(Neg(Infinity), 0)), And(Element(z, CC), Greater(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