Fungrim entry: 59a5d6

\operatorname{csgn}(z) = \begin{cases} \operatorname{sgn}\!\left(\operatorname{Im}(z)\right), & \operatorname{Re}(z) = 0\\\operatorname{sgn}\!\left(\operatorname{Re}(z)\right), & \text{otherwise}\\ \end{cases}

Assumptions:

z \in \mathbb{C}

TeX:

\operatorname{csgn}(z) = \begin{cases} \operatorname{sgn}\!\left(\operatorname{Im}(z)\right), & \operatorname{Re}(z) = 0\\\operatorname{sgn}\!\left(\operatorname{Re}(z)\right), & \text{otherwise}\\ \end{cases}

z \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`Csgn`	$\operatorname{csgn}(z)$	Real-valued sign function for complex numbers
`Sign`	$\operatorname{sgn}(z)$	Sign function
`Im`	$\operatorname{Im}(z)$	Imaginary part
`Re`	$\operatorname{Re}(z)$	Real part
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("59a5d6"),
    Formula(Equal(Csgn(z), Cases(Tuple(Sign(Im(z)), Equal(Re(z), 0)), Tuple(Sign(Re(z)), Otherwise)))),
    Variables(z),
    Assumptions(Element(z, CC)))

Topics using this entry

Complex parts