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Fungrim entry: d40229

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

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, c \in \left[0, \infty\right) \,\mathbin{\operatorname{and}}\, z + c \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("d40229"),
    Formula(Equal(Sqrt(Div(z, Add(z, c))), Div(Sqrt(z), Sqrt(Add(z, c))))),
    Variables(z, c),
    Assumptions(And(Element(z, CC), Element(c, ClosedOpenInterval(0, Infinity)), Unequal(Add(z, c), 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