Csgn

The complex sign function -- $1$ in the right half-plane, $-1$ in the left, and on the imaginary axis the sign of the imaginary part; $0$ at the origin.

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Csgn(z)broadcasts element-wise over a list, like compute-engine's other numeric heads

Typed signatures

Type	Package	Applies
(number) -> number	analytic	always

Domain: Elementary functions

Plot

Examples

Basic #

live ↗

In$\mathrm{Csgn}(1)$Out$1$

Exact for a negative integer, no N() needed

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In$\mathrm{Csgn}(-3)$Out$-1$

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In$\mathrm{Csgn}(0)$Out$0$

Scope #

$\mathrm{Csgn}(i) = 1$ -- $\mathrm{Re}(i) = 0$ and $\mathrm{Im}(i) > 0$

live ↗

In$N(\mathrm{Csgn}(i))$Out$1.0$

$\mathrm{Csgn}(-i) = -1$ -- $\mathrm{Re}(-i) = 0$ and $\mathrm{Im}(-i) < 0$

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In$N(\mathrm{Csgn}(-i))$Out$-1.0$

About

Examples	5
Crosswalk	FungrimFungrim entry ×4

See also: RealSign, Sign