# Fungrim entry: 500c0a

$\operatorname{atan}(z) = \frac{i}{2} \log\!\left(\frac{1 - i z}{1 + i z}\right)$
Assumptions:$z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; -z i \notin \left[1, \infty\right)$
TeX:
\operatorname{atan}(z) = \frac{i}{2} \log\!\left(\frac{1 - i z}{1 + i z}\right)

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; -z i \notin \left[1, \infty\right)
Definitions:
Fungrim symbol Notation Short description
Atan$\operatorname{atan}(z)$ Inverse tangent
ConstI$i$ Imaginary unit
Log$\log(z)$ Natural logarithm
CC$\mathbb{C}$ Complex numbers
ClosedOpenInterval$\left[a, b\right)$ Closed-open interval
Infinity$\infty$ Positive infinity
Source code for this entry:
Entry(ID("500c0a"),
Formula(Equal(Atan(z), Mul(Div(ConstI, 2), Log(Div(Sub(1, Mul(ConstI, z)), Add(1, Mul(ConstI, z))))))),
Variables(z),
Assumptions(And(Element(z, CC), NotElement(Mul(Neg(z), ConstI), ClosedOpenInterval(1, Infinity)))))

## 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