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

z \in \mathbb{C} \setminus \left\{-i, i\right\}
Fungrim symbol Notation Short description
SolutionssolutionsxSQ(x)\mathop{\operatorname{solutions}\,}\limits_{x \in S} Q(x) Solution set
CCC\mathbb{C} Complex numbers
Atanatan(z)\operatorname{atan}(z) Inverse tangent
Piπ\pi The constant pi (3.14...)
ZZZ\mathbb{Z} Integers
ConstIii Imaginary unit
Source code for this entry:
    Formula(Equal(Solutions(Brackets(Equal(Tan(w), z)), ForElement(w, CC)), Set(Add(Atan(z), Mul(Pi, n)), ForElement(n, ZZ)))),
    Assumptions(Element(z, SetMinus(CC, Set(Neg(ConstI), ConstI)))))

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2021-03-15 19:12:00.328586 UTC