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.
NOTE To use Complex, you must explicitly import it with require "complex"
require "complex"
Complex.new(1, 0) # => 1.0 + 0.0.i
Complex.new(5, -12) # => 5.0 - 12.0.i
1.to_c # => 1.0 + 0.0.i
1.i # => 0.0 + 1.0.i
Defined in:
complex.crConstructors
- .additive_identity : self
- .multiplicative_identity : self
- .new(real : Number, imag : Number = 0)
- .new(c : Complex)
-
.zero : Complex
Returns the number
0in complex form.
Instance Method Summary
-
#*(other : Complex) : Complex
Multiplies
selfby other. -
#*(other : Number) : Complex
Multiplies
selfby other. -
#+(other : Complex) : Complex
Adds the value of
selfto other. -
#+(other : Number) : Complex
Adds the value of
selfto other. -
#+ : Complex
Returns
self. -
#-(other : Complex) : Complex
Removes the value of other from
self. -
#-(other : Number) : Complex
Removes the value of other from
self. -
#- : Complex
Returns the opposite of
self. -
#/(other : Complex) : Complex
Divides
selfby other. -
#/(other : Number) : Complex
Divides
selfby other. -
#==(other : Complex)
Determines whether
selfequals other or not. -
#==(other : Number)
Determines whether
selfequals other or not. -
#==(other)
Determines whether
selfequals other or not. -
#abs : Float64
Returns the absolute value of this complex number in a number form, using the Pythagorean theorem.
-
#abs2 : Float64
Returns the square of absolute value in a number form.
- #clone
-
#conj : Complex
Returns the conjugate of
self. - #hash(hasher)
-
#imag : Float64
Returns the imaginary part.
-
#inspect(io : IO) : Nil
Writes this complex object to an io, surrounded by parentheses.
-
#inv : Complex
Returns the inverse of
self. -
#phase : Float64
Returns the phase of
self. - #polar : Tuple(Float64, Float64)
-
#real : Float64
Returns the real part.
-
#round(digits = 0) : Complex
Rounds to the nearest digits.
-
#sign : Complex
Returns the complex sign of
self. -
#to_c
Returns
self. -
#to_f
See
#to_f64. - #to_f32(*args, **options)
- #to_f32(*args, **options, &)
-
#to_f64 : Float64
Returns the value as a
Float64if possible (the imaginary part should be exactly zero), raises otherwise. -
#to_i
See
#to_i32. - #to_i128(*args, **options)
- #to_i128(*args, **options, &)
- #to_i16(*args, **options)
- #to_i16(*args, **options, &)
- #to_i32(*args, **options)
- #to_i32(*args, **options, &)
- #to_i64(*args, **options)
- #to_i64(*args, **options, &)
- #to_i8(*args, **options)
- #to_i8(*args, **options, &)
-
#to_s(io : IO) : Nil
Writes this complex object to an io.
- #to_u128(*args, **options)
- #to_u128(*args, **options, &)
- #to_u16(*args, **options)
- #to_u16(*args, **options, &)
- #to_u32(*args, **options)
- #to_u32(*args, **options, &)
- #to_u64(*args, **options)
- #to_u64(*args, **options, &)
- #to_u8(*args, **options)
- #to_u8(*args, **options, &)
-
#zero? : Bool
Returns
trueif the complex number is zero.
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?(collection : Object) : Bool
in?(*values : Object) : Bool in?, inspect(io : IO) : Nil
inspect : String inspect, is_a?(type : Class) : Bool is_a?, itself itself, nil? : Bool nil?, not_nil!(message)
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) : Nil
to_json : String to_json, to_pretty_json(indent : String = " ") : String
to_pretty_json(io : IO, indent : String = " ") : Nil to_pretty_json, to_s(io : IO) : Nil
to_s : String to_s, to_yaml(io : IO) : Nil
to_yaml : String 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
Macros inherited from class Object
class_getter(*names, &block)
class_getter,
class_getter!(*names)
class_getter!,
class_getter?(*names, &block)
class_getter?,
class_property(*names, &block)
class_property,
class_property!(*names)
class_property!,
class_property?(*names, &block)
class_property?,
class_setter(*names)
class_setter,
def_clone
def_clone,
def_equals(*fields)
def_equals,
def_equals_and_hash(*fields)
def_equals_and_hash,
def_hash(*fields)
def_hash,
delegate(*methods, to object)
delegate,
forward_missing_to(delegate)
forward_missing_to,
getter(*names, &block)
getter,
getter!(*names)
getter!,
getter?(*names, &block)
getter?,
property(*names, &block)
property,
property!(*names)
property!,
property?(*names, &block)
property?,
setter(*names)
setter
Constructor Detail
Instance Method Detail
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
Returns the square of absolute value in a number form.
require "complex"
Complex.new(42, 2).abs2 # => 1768
Returns the conjugate of self.
require "complex"
Complex.new(42, 2).conj # => 42.0 - 2.0.i
Complex.new(42, -2).conj # => 42.0 + 2.0.i
Writes this complex object to an io, surrounded by parentheses.
require "complex"
Complex.new(42, 2).inspect # => "(42.0 + 2.0i)"
Returns a Tuple with the #abs value and the #phase.
require "complex"
Complex.new(42, 2).polar # => {42.047592083257278, 0.047583103276983396}
Returns the complex sign of self.
If self is non-zero, the returned value has the same phase as self and
absolute value 1.0. If self is zero, returns self.
The returned value's real and imaginary components always have the same
signs as the respective components of self.
require "complex"
Complex.new(7, -24).sign # => (0.28 - 0.96.i)
Complex.new(1.0 / 0.0, 24).sign # => (1.0 + 0.0.i)
Complex.new(-0.0, +0.0).sign # => (-0.0 + 0.0.i)
Returns the value as a Float64 if possible (the imaginary part should be exactly zero),
raises otherwise.
Writes this complex object to an io.
require "complex"
Complex.new(42, 2).to_s # => "42.0 + 2.0i"