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Fungrim entry: e0ac95

zeros⁡ z∈C(z2−c)={i−c,−i−c}\mathop{\operatorname{zeros}\,}\limits_{z \in \mathbb{C}} \left({z}^{2} - c\right) = \left\{i \sqrt{-c}, -i \sqrt{-c}\right\}
Assumptions:c∈Cc \in \mathbb{C}
TeX:
\mathop{\operatorname{zeros}\,}\limits_{z \in \mathbb{C}} \left({z}^{2} - c\right) = \left\{i \sqrt{-c}, -i \sqrt{-c}\right\}

c \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Powab{a}^{b} Power
CCC\mathbb{C} Complex numbers
ConstIii Imaginary unit
Sqrtz\sqrt{z} Principal square root
Source code for this entry:
Entry(ID("e0ac95"),
    Formula(Equal(Zeros(Sub(Pow(z, 2), c), z, Element(z, CC)), Set(Mul(ConstI, Sqrt(Neg(c))), Mul(Neg(ConstI), Sqrt(Neg(c)))))),
    Variables(c),
    Assumptions(Element(c, CC)))

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