Fungrim entry: 54340e

\operatorname{sgn}\!\left(z\right) = \exp\!\left(i \arg\!\left(z\right)\right)

Assumptions:

z \in \mathbb{C} \setminus \left\{0\right\}

TeX:

\operatorname{sgn}\!\left(z\right) = \exp\!\left(i \arg\!\left(z\right)\right)

z \in \mathbb{C} \setminus \left\{0\right\}

Definitions:

Fungrim symbol	Notation	Short description
`Sign`	$\operatorname{sgn}\!\left(z\right)$	Sign function
`Exp`	${e}^{z}$	Exponential function
`ConstI`	$i$	Imaginary unit
`Arg`	$\arg\!\left(z\right)$	Complex argument
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("54340e"),
    Formula(Equal(Sign(z), Exp(Mul(ConstI, Arg(z))))),
    Variables(z),
    Assumptions(Element(z, SetMinus(CC, Set(0)))))

Topics using this entry

2019-06-18 07:49:59.356594 UTC