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Fungrim entry: 185efc

zc−z=z1c−z\sqrt{\frac{z}{c - z}} = \sqrt{z} \sqrt{\frac{1}{c - z}}
Assumptions:z∈C and⁡ c∈[0,∞) and⁡ c−z≠0z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, c \in \left[0, \infty\right) \,\mathbin{\operatorname{and}}\, c - z \ne 0
TeX:
\sqrt{\frac{z}{c - z}} = \sqrt{z} \sqrt{\frac{1}{c - z}}

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, c \in \left[0, \infty\right) \,\mathbin{\operatorname{and}}\, c - z \ne 0
Definitions:
Fungrim symbol Notation Short description
Sqrtz\sqrt{z} Principal square root
CCC\mathbb{C} Complex numbers
ClosedOpenInterval[a,b)\left[a, b\right) Closed-open interval
Infinity∞\infty Positive infinity
Source code for this entry:
Entry(ID("185efc"),
    Formula(Equal(Sqrt(Div(z, Sub(c, z))), Mul(Sqrt(z), Sqrt(Div(1, Sub(c, z)))))),
    Variables(z, c),
    Assumptions(And(Element(z, CC), Element(c, ClosedOpenInterval(0, Infinity)), Unequal(Sub(c, z), 0))))

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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