Imaginary

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Imaginary () is a monadic scalar function which multiplies the argument by the imaginary unit 0J1, usually denoted or in traditional mathematics. 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

See also

External links

Documentation

APL built-ins [edit]
Primitives (Timeline) Functions
Scalar
Monadic ConjugateNegateSignumReciprocalMagnitudeExponentialNatural LogarithmFloorCeilingFactorialNotPi TimesRollTypeImaginarySquare Root
Dyadic AddSubtractTimesDivideResiduePowerLogarithmMinimumMaximumBinomialComparison functionsBoolean functions (And, Or, Nand, Nor) ∙ GCDLCMCircularComplexRoot
Non-Scalar
Structural ShapeReshapeTallyDepthRavelEnlistTableCatenateReverseRotateTransposeRazeMixSplitEncloseNestCut (K)PairLinkPartitioned EnclosePartition
Selection FirstPickTakeDropUniqueIdentityStopSelectReplicateExpandSet functions (IntersectionUnionWithout) ∙ Bracket indexingIndexCartesian ProductSort
Selector Index generatorGradeIndex OfInterval IndexIndicesDealPrefix and suffix vectors
Computational MatchNot MatchMembershipFindNub SieveEncodeDecodeMatrix InverseMatrix DivideFormatExecuteMaterialiseRange
Operators Monadic EachCommuteConstantReplicateExpandReduceWindowed ReduceScanOuter ProductKeyI-BeamSpawnFunction axis
Dyadic BindCompositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner ProductDeterminantPowerAtUnderRankDepthVariantStencilCutDirect definition (operator)
Quad names Index originComparison toleranceMigration levelAtomic vector