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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
Zeroszeros⁡ x∈Sf(x)\mathop{\operatorname{zeros}\,}\limits_{x \in S} f(x) Zeros (roots) of function
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), ForElement(z, CC)), Set(Mul(ConstI, Sqrt(Neg(c))), Mul(Neg(ConstI), Sqrt(Neg(c)))))),
    Variables(c),
    Assumptions(Element(c, CC)))

Topics using this entry

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2021-03-15 19:12:00.328586 UTC