The library documents itself · Numeric & optimization

stzComplex

19 own methods · 8 forms written with extensions, listed under their method

the source: base/number/stzComplex.ring(opens in a new tab) · All classes · The area reference: Numeric & optimization

Under each method, its extensions (Q CS XT Z ZZ IB W U): bold and ticked, it exists; struck, it does not. The extensions and what they mean

Examples: 0 come from the library's tests; 9 were composed from each method's signature and run for this page, on a fresh object, for example o1 = new stzComplex(1, -2). 10 methods have none yet. Examples run on 2026-10-03 12:54 inside the library at commit 0e72e2e2c.

Method

Explanation, as the source carries it

init

(no comment in the source: the name reads as a sentence) initno extension

RealPart

(no comment in the source: the name reads as a sentence) real part

composed example

o1 = new stzComplex(1, -2)
? o1.RealPart()
#--> 1

composed from the signature, run for this page

no extension

ImaginaryPart

(no comment in the source: the name reads as a sentence) imaginary part 1 examples run

composed example

o1 = new stzComplex(1, -2)
? o1.ImaginaryPart()
#--> -2

composed from the signature, run for this page

no extension

Parts

(no comment in the source: the name reads as a sentence) parts

composed example

o1 = new stzComplex(1, -2)
? @@( o1.Parts() )
#--> [ 1, -2 ]

composed from the signature, run for this page

no extension

Content

"3+4i", "3-4i", "3" when the imaginary part is zero, "4i" when the real part isno extension

IsReal

(no comment in the source: the name reads as a sentence) is real

composed example

o1 = new stzComplex(1, -2)
? o1.IsReal()
#--> 0

composed from the signature, run for this page

no extension

IsImaginary

(no comment in the source: the name reads as a sentence) is imaginary

composed example

o1 = new stzComplex(1, -2)
? o1.IsImaginary()
#--> 0

composed from the signature, run for this page

no extension

IsZero

(no comment in the source: the name reads as a sentence) is zero

composed example

o1 = new stzComplex(1, -2)
? o1.IsZero()
#--> 0

composed from the signature, run for this page

no extension

Modulus

|z|. Via the hypotenuse rather than sqrt(re^2 + im^2), which overflows for parts above about 1e154 on values the answer handles perfectly well.also written: Magnitudeno extension

Argument

the angle from the positive real axis, in (-pi, pi]no extension

Conjugate

An ACTIVE verb mutates this number and returns nothing; the PASSIVE ...ed form returns the [re, im] DATA and leaves it alone; the Q twin returns a new stzComplex so calls chain. The first version of this class had Conjugate() and Negated() both returning new objects from plain names, which breaks the rule that a plain method returns data and only a Q form returns a Softanza object. 1 examples runQCSXTZZZIBWU

Conjugated

(no comment in the source: the name reads as a sentence) conjugated 1 examples run

composed example

o1 = new stzComplex(1, -2)
? @@( o1.Conjugated() )
#--> [ 1, 2 ]

composed from the signature, run for this page

QCSXTZZZIBWU

Negate

(no comment in the source: the name reads as a sentence) negate

composed example

o1 = new stzComplex(1, -2)
o1.Negate()
? o1.Content()
#--> -1+2i

composed from the signature, run for this page

QCSXTZZZIBWU

Negated

(no comment in the source: the name reads as a sentence) negated

composed example

o1 = new stzComplex(1, -2)
? @@( o1.Negated() )
#--> [ -1, 2 ]

composed from the signature, run for this page

QCSXTZZZIBWU

Plus

── arithmetic: DATA out, or a chainable object from the Q twin ── 1 examples runQCSXTZZZIBWU

Minus

(no comment in the source: the name reads as a sentence) minusQCSXTZZZIBWU

Times

(no comment in the source: the name reads as a sentence) times 1 examples runQCSXTZZZIBWU

DividedBy

Smith's formula, for the same overflow reason as Modulus(): dividing through by the larger part first keeps the intermediates near 1. 1 examples runQCSXTZZZIBWU

Equals

(no comment in the source: the name reads as a sentence) equalsno extension