Fungrim entry: 8cac46

\arg\!\left(c z\right) = \arg(z)

Assumptions:

z \in \mathbb{C} \setminus \left\{0\right\} \;\mathbin{\operatorname{and}}\; c \in \left(0, \infty\right)

TeX:

\arg\!\left(c z\right) = \arg(z)

z \in \mathbb{C} \setminus \left\{0\right\} \;\mathbin{\operatorname{and}}\; c \in \left(0, \infty\right)

Definitions:

Fungrim symbol	Notation	Short description
`Arg`	$\arg(z)$	Complex argument
`CC`	$\mathbb{C}$	Complex numbers
`OpenInterval`	$\left(a, b\right)$	Open interval
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("8cac46"),
    Formula(Equal(Arg(Mul(c, z)), Arg(z))),
    Variables(z, c),
    Assumptions(And(Element(z, SetMinus(CC, Set(0))), Element(c, OpenInterval(0, Infinity)))))

Topics using this entry

Complex parts

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