Programmer's Guide & Language Reference - Dyalog Limited

Chapter 1: Introduction 24The absolute value, or magnitude of a complex number is naturally obtained usingthe Magnitude function5|3j4Monadic + of a complex number (a+bi) returns its conjugate (a-bi) ...3J¯4+3j4... which when multiplied by the complex number itself, produces the square of itsmagnitude.253j4×3j¯4Furthermore, adding a complex number and its conjugate produces a real number:63j4+3j¯4iπThe famous Euler's Identitye + 1 = 001+*○0j1 ⍝ Euler IdentityDifferent Result for Powermay be expressed as follows:IFrom Version 13.0 onwards , the implementation of X*Y (Power) gives a differentanswer for negative real X than in all previous Versions of Dyalog APL. This changeis however in accordance with the ISO/EEC 13751 Standard for Extended APL.In Version 13.0 onwards, the result is the principal value; whereas in previous Versionsthe result is a negative or positive real number or DOMAIN ERROR. The followingexamples illustrate this point:¯8 * 1 2 ÷ 3 ⍝ Version 12.1¯2 4¯8 * 1 2 ÷ 3 ⍝ Version 13.01J1.732050808 ¯2J3.464101615* (1 2 ÷ 3) × ⍟ ¯8 ⍝ Version 13.01J1.732050808 ¯2J3.464101615