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Fungrim entry: 8cac46

arg ⁣(cz)=arg ⁣(z)\arg\!\left(c z\right) = \arg\!\left(z\right)
Assumptions:zC{0}andc(0,)z \in \mathbb{C} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, c \in \left(0, \infty\right)
\arg\!\left(c z\right) = \arg\!\left(z\right)

z \in \mathbb{C} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, c \in \left(0, \infty\right)
Fungrim symbol Notation Short description
Argarg ⁣(z)\arg\!\left(z\right) Complex argument
CCC\mathbb{C} Complex numbers
OpenInterval(a,b)\left(a, b\right) Open interval
Infinity\infty Positive infinity
Source code for this entry:
    Formula(Equal(Arg(Mul(c, z)), Arg(z))),
    Variables(z, c),
    Assumptions(And(Element(z, SetMinus(CC, Set(0))), Element(c, OpenInterval(0, Infinity)))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-09-15 14:14:26.267625 UTC