# Fungrim entry: cbce7f

$\mathop{\operatorname{solutions}\,}\limits_{w \in \mathbb{C}} \left[\tan(w) = z\right] = \left\{ \operatorname{atan}(z) + \pi n : n \in \mathbb{Z} \right\}$
Assumptions:$z \in \mathbb{C} \setminus \left\{-i, i\right\}$
TeX:
\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\}
Definitions:
Fungrim symbol Notation Short description
Solutions$\mathop{\operatorname{solutions}\,}\limits_{x \in S} Q(x)$ Solution set
CC$\mathbb{C}$ Complex numbers
Atan$\operatorname{atan}(z)$ Inverse tangent
Pi$\pi$ 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)), ForElement(w, CC)), Set(Add(Atan(z), Mul(Pi, n)), ForElement(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.

2021-03-15 19:12:00.328586 UTC