Fungrim entry: cbce7f

\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:

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
`CC`	$\mathbb{C}$	Complex numbers
`SetBuilder`	$\left\{ f\!\left(x\right) : P\!\left(x\right) \right\}$	Set comprehension
`Atan`	$\operatorname{atan}\!\left(z\right)$	Inverse tangent
`ConstPi`	$\pi$	The constant pi (3.14...)
`ZZ`	$\mathbb{Z}$	Integers
`ConstI`	$i$	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)))))

Topics using this entry

Inverse tangent