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Fungrim entry: cbce7f

solutionswC[tan ⁣(w)=z]={atan ⁣(z)+πn:nZ}\mathop{\operatorname{solutions}\,}\limits_{w \in \mathbb{C}} \left[\tan\!\left(w\right) = z\right] = \left\{ \operatorname{atan}\!\left(z\right) + \pi n : n \in \mathbb{Z} \right\}
Assumptions:zC{i,i}z \in \mathbb{C} \setminus \left\{-i, i\right\}
TeX:
\mathop{\operatorname{solutions}\,}\limits_{w \in \mathbb{C}} \left[\tan\!\left(w\right) = z\right] = \left\{ \operatorname{atan}\!\left(z\right) + \pi n : n \in \mathbb{Z} \right\}

z \in \mathbb{C} \setminus \left\{-i, i\right\}
Definitions:
Fungrim symbol Notation Short description
SolutionssolutionsP(x)Q ⁣(x)\mathop{\operatorname{solutions}\,}\limits_{P\left(x\right)} Q\!\left(x\right) Solution set
CCC\mathbb{C} Complex numbers
SetBuilder{f ⁣(x):P ⁣(x)}\left\{ f\!\left(x\right) : P\!\left(x\right) \right\} Set comprehension
Atanatan ⁣(z)\operatorname{atan}\!\left(z\right) Inverse tangent
ConstPiπ\pi The constant pi (3.14...)
ZZZ\mathbb{Z} Integers
ConstIii Imaginary unit
Source code for this entry:
Entry(ID("cbce7f"),
    Formula(Equal(Solutions(Brackets(Equal(Tan(w), z)), w, Element(w, CC)), SetBuilder(Add(Atan(z), Mul(ConstPi, n)), n, Element(n, ZZ)))),
    Variables(z),
    Assumptions(Element(z, SetMinus(CC, Set(Neg(ConstI), ConstI)))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-09-16 21:17:18.797188 UTC