# Fungrim entry: e0ac95

$\mathop{\operatorname{zeros}\,}\limits_{z \in \mathbb{C}} \left({z}^{2} - c\right) = \left\{i \sqrt{-c}, -i \sqrt{-c}\right\}$
Assumptions:$c \in \mathbb{C}$
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
Zeros$\mathop{\operatorname{zeros}\,}\limits_{P\left(x\right)} f\!\left(x\right)$ Zeros (roots) of function
Pow${a}^{b}$ Power
CC$\mathbb{C}$ Complex numbers
ConstI$i$ Imaginary unit
Sqrt$\sqrt{z}$ 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.

2019-08-21 11:44:15.926409 UTC