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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.


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       3 ¯4 6
0J3 0J¯4 0J6



APL built-ins [edit]
Primitive functions
Monadic ConjugateNegateSignumReciprocalMagnitudeExponentialNatural LogarithmFloorCeilingFactorialNotPi TimesRollTypeImaginarySquare Root
Dyadic AddSubtractTimesDivideResiduePowerLogarithmMinimumMaximumBinomialComparison functionsBoolean functions (And, Or, Nand, Nor) ∙ GCDLCMCircularComplexRoot
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)
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Arrays Index originMigration levelAtomic vector
Functions Name classCase convertUnicode convert
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