struct Complex

Overview

A complex number is a number represented in the form a + bi. In this form, a and b are real numbers, and i is an imaginary number such as i² = -1. The a is the real part of the number, and the b is the imaginary part of the number.

require "complex"

Complex.new(1, 0)   # => 1.0 + 0.0i
Complex.new(5, -12) # => 5.0 - 12.0i

1.to_c # => 1.0 + 0.0i
1.i    # => 0.0 + 1.0i

Defined in:

complex.cr

Constructors

Instance Method Summary

Instance methods inherited from struct Struct

==(other) : Bool ==, hash(hasher) hash, inspect(io : IO) : Nil inspect, pretty_print(pp) : Nil pretty_print, to_s(io : IO) : Nil to_s

Instance methods inherited from struct Value

==(other : JSON::Any)
==(other : YAML::Any)
==(other)
==
, dup dup

Instance methods inherited from class Object

! : Bool !, !=(other) !=, !~(other) !~, ==(other) ==, ===(other : JSON::Any)
===(other : YAML::Any)
===(other)
===
, =~(other) =~, as(type : Class) as, as?(type : Class) as?, class class, dup dup, hash(hasher)
hash
hash
, in?(*values : Object) : Bool
in?(collection) : Bool
in?
, inspect : String
inspect(io : IO) : Nil
inspect
, is_a?(type : Class) : Bool is_a?, itself itself, nil? : Bool nil?, not_nil! not_nil!, pretty_inspect(width = 79, newline = "\n", indent = 0) : String pretty_inspect, pretty_print(pp : PrettyPrint) : Nil pretty_print, responds_to?(name : Symbol) : Bool responds_to?, tap(&) tap, to_json(io : IO)
to_json
to_json
, to_pretty_json(io : IO, indent : String = " ")
to_pretty_json(indent : String = " ")
to_pretty_json
, to_s : String
to_s(io : IO) : Nil
to_s
, to_yaml(io : IO)
to_yaml
to_yaml
, try(&) try, unsafe_as(type : T.class) forall T unsafe_as

Class methods inherited from class Object

from_json(string_or_io, root : String)
from_json(string_or_io)
from_json
, from_yaml(string_or_io : String | IO) from_yaml

Constructor Detail

def self.additive_identity : self #

[View source]
def self.new(real : Number, imag : Number = 0) #

[View source]
def self.new(c : Complex) #

[View source]
def self.zero : Complex #

Returns the number 0 in complex form.


[View source]

Instance Method Detail

def *(other : Complex) #

Multiplies self by other.


[View source]
def *(other : Number) #

Multiplies self by other.


[View source]
def +(other : Complex) #

Adds the value of self to other.


[View source]
def +(other : Number) #

Adds the value of self to other.


[View source]
def + #

Returns self.


[View source]
def - #

Returns the opposite of self.


[View source]
def -(other : Complex) #

Removes the value of other from self.


[View source]
def -(other : Number) #

Removes the value of other from self.


[View source]
def /(other : Complex) #

Divides self by other.


[View source]
def /(other : Number) #

Divides self by other.


[View source]
def ==(other) #

Determines whether self equals other or not.


[View source]
def ==(other : Number) #

Determines whether self equals other or not.


[View source]
def ==(other : Complex) #

Determines whether self equals other or not.


[View source]
def abs #

Returns the absolute value of this complex number in a number form, using the Pythagorean theorem.

require "complex"

Complex.new(42, 2).abs  # => 42.04759208325728
Complex.new(-42, 2).abs # => 42.04759208325728

[View source]
def abs2 #

Returns the square of absolute value in a number form.

require "complex"

Complex.new(42, 2).abs2 # => 1768

[View source]
def clone #

[View source]
def conj #

Returns the conjugate of self.

require "complex"

Complex.new(42, 2).conj  # => 42.0 - 2.0i
Complex.new(42, -2).conj # => 42.0 + 2.0i

[View source]
def hash(hasher) #

[View source]
def imag : Float64 #

Returns the imaginary part.


[View source]
def inspect(io : IO) : Nil #

Writes this complex object to an io, surrounded by parentheses.

require "complex"

Complex.new(42, 2).inspect # => "(42.0 + 2.0i)"

[View source]
def inv #

Returns the inverse of self.


[View source]
def multiplicative_identity : self #

[View source]
def phase #

Returns the phase of self.


[View source]
def polar #

Returns a Tuple with the #abs value and the #phase.

require "complex"

Complex.new(42, 2).polar # => {42.047592083257278, 0.047583103276983396}

[View source]
def real : Float64 #

Returns the real part.


[View source]
def round(digits = 0) #

Rounds to the nearest digits.


[View source]
def sign #

[View source]
def to_c #

Returns self.


[View source]
def to_f #

See #to_f64.


[View source]
def to_f32 #

Returns the value as a Float32 if possible (the imaginary part should be exactly zero), raises otherwise.


[View source]
def to_f64 #

Returns the value as a Float64 if possible (the imaginary part should be exactly zero), raises otherwise.


[View source]
def to_i #

See #to_i32.


[View source]
def to_i16(*args, **options) #

[View source]
def to_i16(*args, **options, &) #

[View source]
def to_i32(*args, **options) #

[View source]
def to_i32(*args, **options, &) #

[View source]
def to_i64 #

Returns the value as an Int64 if possible (the imaginary part should be exactly zero), raises otherwise.


[View source]
def to_i8(*args, **options) #

[View source]
def to_i8(*args, **options, &) #

[View source]
def to_s(io : IO) : Nil #

Writes this complex object to an io.

require "complex"

Complex.new(42, 2).to_s # => "42.0 + 2.0i"

[View source]
def to_u16(*args, **options) #

[View source]
def to_u16(*args, **options, &) #

[View source]
def to_u32(*args, **options) #

[View source]
def to_u32(*args, **options, &) #

[View source]
def to_u64 #

Returns the value as an UInt64 if possible (the imaginary part should be exactly zero), raises otherwise.


[View source]
def to_u8(*args, **options) #

[View source]
def to_u8(*args, **options, &) #

[View source]
def zero? : Bool #

[View source]