Imaginary

Imaginary (⌾) is a monadic scalar function which multiplies the argument by the imaginary unit <source lang=apl inline>0J1</syntaxhighlight>, usually denoted $i$ or $j$ 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 <source lang=j inline>j.</syntaxhighlight> together with initial support for complex numbers, and was adopted in Extended Dyalog APL using the glyph <source lang=apl inline>⌾</syntaxhighlight> as a monadic counterpart of Complex. In other APL implementations that support complex numbers, Circular with the left argument of <source lang=apl inline>¯11</syntaxhighlight> has the same functionality as Imaginary.

Examples

Try it online!<source lang=apl>

     ⌾ 3 ¯4 6

0J3 0J¯4 0J6

</syntaxhighlight>

Works in: Extended Dyalog APL

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

Try it online!<source lang=apl>

     0 ⌾ 3 ¯4 6

0J3 0J¯4 0J6

</syntaxhighlight>

Works in: Extended Dyalog APL

External links

Documentation

J Dictionary, NuVoc

APL built-ins [edit]
Primitives (Timeline)	Functions
Scalar
		Monadic	Conjugate ∙ Negate ∙ Signum ∙ Reciprocal ∙ Magnitude ∙ Exponential ∙ Natural Logarithm ∙ Floor ∙ Ceiling ∙ Factorial ∙ Not ∙ Pi Times ∙ Roll ∙ Type ∙ Imaginary ∙ Square Root
		Dyadic	Add ∙ Subtract ∙ Times ∙ Divide ∙ Residue ∙ Power ∙ Logarithm ∙ Minimum ∙ Maximum ∙ Binomial ∙ Comparison functions ∙ Boolean functions (And, Or, Nand, Nor) ∙ GCD ∙ LCM ∙ Circular ∙ Complex ∙ Root
Non-Scalar
		Structural	Shape ∙ Reshape ∙ Tally ∙ Depth ∙ Ravel ∙ Enlist ∙ Table ∙ Catenate ∙ Reverse ∙ Rotate ∙ Transpose ∙ Raze ∙ Mix ∙ Split ∙ Enclose ∙ Nest ∙ Cut (K) ∙ Pair ∙ Link ∙ Partitioned Enclose ∙ Partition
		Selection	First ∙ Pick ∙ Take ∙ Drop ∙ Unique ∙ Identity ∙ Stop ∙ Select ∙ Replicate ∙ Expand ∙ Set functions (Intersection ∙ Union ∙ Without) ∙ Bracket indexing ∙ Index ∙ Cartesian Product ∙ Sort
		Selector	Index generator ∙ Grade ∙ Index Of ∙ Interval Index ∙ Indices ∙ Deal ∙ Prefix and suffix vectors
		Computational	Match ∙ Not Match ∙ Membership ∙ Find ∙ Nub Sieve ∙ Encode ∙ Decode ∙ Matrix Inverse ∙ Matrix Divide ∙ Format ∙ Execute ∙ Materialise ∙ Range
Operators	Monadic	Each ∙ Commute ∙ Constant ∙ Replicate ∙ Expand ∙ Reduce ∙ Windowed Reduce ∙ Scan ∙ Outer Product ∙ Key ∙ I-Beam ∙ Spawn ∙ Function axis
Operators	Dyadic	Bind ∙ Compositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner Product ∙ Determinant ∙ Power ∙ At ∙ Under ∙ Rank ∙ Depth ∙ Variant ∙ Stencil ∙ Cut ∙ Direct definition (operator)
Quad names	Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector

Imaginary

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Imaginary

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