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# Fungrim entry: 6f63dd

$\sqrt{\frac{z}{z - c}} = \frac{\sqrt{-z}}{\sqrt{c - z}}$
Assumptions:$z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; c \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; z - c \ne 0$
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
Sqrt$\sqrt{z}$ Principal square root
CC$\mathbb{C}$ Complex numbers
ClosedOpenInterval$\left[a, b\right)$ 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