Fungrim entry: caf706

\operatorname{sgn}\!\left({e}^{z}\right) = \exp\!\left(\operatorname{Im}\!\left(z\right) i\right)

Assumptions:

z \in \mathbb{C}

TeX:

\operatorname{sgn}\!\left({e}^{z}\right) = \exp\!\left(\operatorname{Im}\!\left(z\right) i\right)

z \in \mathbb{C}

Definitions:

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

Source code for this entry:

Entry(ID("caf706"),
    Formula(Equal(Sign(Exp(z)), Exp(Mul(Im(z), ConstI)))),
    Variables(z),
    Assumptions(Element(z, CC)))

Topics using this entry

2019-06-18 07:49:59.356594 UTC