# Imaginary

 `⌾`

Imaginary (`⌾`) is a monadic scalar function which multiplies the argument by the imaginary unit `0J1`. This can be seen as a mapping from a real number to a pure imaginary number (a complex number with the real part of 0). It was added to J as `j.` together with initial support for complex numbers, and was adopted in Extended Dyalog APL using the glyph `⌾` as a monadic counterpart of Complex. In other APL implementations that support complex numbers, Circular with the left argument of `¯11` has the same functionality as Imaginary.

## Examples

Try it online!

```      ⌾ 3 ¯4 6
0J3 0J¯4 0J6
```

Imaginary is equivalent to Complex with the default left argument of 0.

Try it online!

```      0 ⌾ 3 ¯4 6
0J3 0J¯4 0J6
```

## References

APL built-ins 
Primitive functions
Scalar
Monadic ConjugateNegateSignumReciprocalMagnitudeExponentialNatural LogarithmFloorCeilingFactorialNotPi TimesRollTypeImaginarySquare Root
Dyadic AddSubtractTimesDivideResiduePowerLogarithmMinimumMaximumBinomialComparison functionsBoolean functions (And, Or, Nand, Nor) ∙ GCDLCMCircularComplexRoot
Non-Scalar
Structural ShapeReshapeTallyDepthRavelEnlistTableCatenateReverseRotateTransposeRazeMixSplitEncloseNestCut (K)PairLinkPartitioned EnclosePartition
Selection FirstPickTakeDropUniqueIdentitySelectReplicateExpandSet functions (IntersectionUnionWithout) ∙ Bracket indexingIndex
Selector Index generatorGradeIndex OfInterval IndexIndicesDeal
Computational MatchNot MatchMembershipFindNub SieveEncodeDecodeMatrix InverseMatrix DivideFormatExecuteMaterialiseRange
Primitive operators Monadic EachCommuteConstantReplicateExpandReduceWindowed ReduceScanOuter ProductKeyI-beamSpawnFunction axis
Dyadic BindCompositions (Compose, Reverse Compose, Beside, Atop, Over) ∙ Inner ProductPowerAtUnderRankDepthVariantStencilCut (J)