# 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
Solutions$\mathop{\operatorname{solutions}\,}\limits_{P\left(x\right)} Q\!\left(x\right)$ Solution set
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

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