Magnitude
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Magnitude (
), or Absolute Value, is a monadic scalar function which gives the absolute value of a real or complex number. Magnitude shares the glyph 
with the dyadic arithmetic function Residue.
Examples
0 1 2 ¯1 ¯2
0 1 2 1 2
0J2 ¯3J¯4
2 5
Properties
The magnitude of any number is a nonnegative real number.
For real numbers, the magnitude equals the original number times (or divided by, for nonzero numbers) its sign.
v←0 1E¯100 20 1E300 ¯1E¯100 ¯20 ¯1E300
(v)≡v××v
1
(v)=v÷×v
0 1 1 1 1 1 1
For complex numbers, the magnitude is defined as the Euclidean distance from the number 0 on the complex plane.
Dist←{0.5*⍨+.×⍨9 11○⍵} ⍝ Square root of square sum of real and imaginary parts
Dist¨ 0 1J2 ¯3J4
0 2.236067977 5
0 1J2 ¯3J4
0 2.236067977 5
Works in: Dyalog APL
Any real or complex number is equal to the product of its signum and magnitude.
(⊢ ≡ ××) 0 1 1E¯300 ¯2.5 0J3.5 ¯3J¯4
1
Works in: Dyalog APL