Imaginary

Imaginary part of a complex number.

✓ checked against that system · ! checked, with disagreements (hover a chip)FungrimIm✓↗Fungrim entryWolfram LanguageIm✓↗

Imaginary(complex | infinity) -> numberthe imaginary part; of a directed infinity, the infinity of its sign, or 0 when it has none.

SageMathimag_part(complex | infinity)mpmathim(complex | infinity)Juliaenumeratio_ball(imag, complex | infinity)

Typed signatures

Type	Package	Applies
(complex | infinity) -> number	analyticreplaces compute-engine	always
(complex | infinity) -> number	compute-engine	always

Domain: Compute engine

Details

• A Gaussian integer is a complex number with integer parts, so Im and Re read its two coordinates; there is no separate head for them.

Plot

ComplexPlot

real slice

Examples

Basic #

$\operatorname{Im}(3+4i) = 4$

live ↗

In$\Im(3+4i)$Out$4$

Scope #

A Gaussian integer is a complex number with integer parts: $(2+i)(1+3i)=-1+7i$

live ↗

In$\Im((2+i)(1+3i))$Out$7$

Properties #

A real infinity has no imaginary part

live ↗

In$\Im(∞)$Out$0$

About

Examples	3
Checked against	Wolfram Language 3 agreeSageMath 3 agreempmath 3 agreeJulia 2 agree1 error
Crosswalk	FungrimFungrim entry ×31Wolfram LanguageSageMathmpmathJulia

Implementation

mappedmpmathpackages/oracle/src/mappings.ts

mappedsagepackages/oracle/src/mappings.ts

mappedjuliapackages/oracle/src/mappings.ts