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Fungrim entry: 6f63dd

zz−c=−zc−z\sqrt{\frac{z}{z - c}} = \frac{\sqrt{-z}}{\sqrt{c - z}}
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{c - z}}

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("6f63dd"),
    Formula(Equal(Sqrt(Div(z, Sub(z, c))), Div(Sqrt(Neg(z)), Sqrt(Sub(c, z))))),
    Variables(z, c),
    Assumptions(And(Element(z, CC), Element(c, ClosedOpenInterval(0, Infinity)), NotEqual(Sub(z, c), 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