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Imaginary: Difference between revisions
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{{Built-in|Imaginary|⌾}} is a [[monadic]] [[scalar function]] which multiplies the [[argument]] by the [[wikipedia:imaginary unit|imaginary unit]] <source lang=apl inline>0J1</ | {{Built-in|Imaginary|⌾}} is a [[monadic]] [[scalar function]] which multiplies the [[argument]] by the [[wikipedia:imaginary unit|imaginary unit]] <source lang=apl inline>0J1</syntaxhighlight>, usually denoted <math>i</math> or <math>j</math> 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 (function)|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 == | == Examples == | ||
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⌾ 3 ¯4 6 | ⌾ 3 ¯4 6 | ||
0J3 0J¯4 0J6 | 0J3 0J¯4 0J6 | ||
</ | </syntaxhighlight>{{Works in|[[Extended Dyalog APL]]}} | ||
Imaginary is equivalent to [[Complex (function)|Complex]] with the default left argument of 0. | Imaginary is equivalent to [[Complex (function)|Complex]] with the default left argument of 0. | ||
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0 ⌾ 3 ¯4 6 | 0 ⌾ 3 ¯4 6 | ||
0J3 0J¯4 0J6 | 0J3 0J¯4 0J6 | ||
</ | </syntaxhighlight>{{Works in|[[Extended Dyalog APL]]}} | ||
== See also == | == See also == | ||