Fungrim entry: a0d93c

\arg\!\left({e}^{z}\right) = \operatorname{Im}(z)

Assumptions:

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Im}(z) \in \left(-\pi, \pi\right]

TeX:

\arg\!\left({e}^{z}\right) = \operatorname{Im}(z)

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Im}(z) \in \left(-\pi, \pi\right]

Definitions:

Fungrim symbol	Notation	Short description
`Arg`	$\arg(z)$	Complex argument
`Exp`	${e}^{z}$	Exponential function
`Im`	$\operatorname{Im}(z)$	Imaginary part
`CC`	$\mathbb{C}$	Complex numbers
`OpenClosedInterval`	$\left(a, b\right]$	Open-closed interval
`Pi`	$\pi$	The constant pi (3.14...)

Source code for this entry:

Entry(ID("a0d93c"),
    Formula(Equal(Arg(Exp(z)), Im(z))),
    Variables(z),
    Assumptions(And(Element(z, CC), Element(Im(z), OpenClosedInterval(Neg(Pi), Pi)))))

Topics using this entry

Exponential function

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