struct Complex

• Complex
• Struct
• Value
• Object

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:

Constructors

• .additive_identity : self
• .multiplicative_identity : self
• .new(real : Number, imag : Number = 0)
• .new(c : Complex)
• .zero : Complex

  Returns the number 0 in complex form.

Instance Method Summary

• #*(other : Complex) : Complex

  Multiplies self by other.

• #*(other : Number) : Complex

  Multiplies self by other.

• #+(other : Complex) : Complex

  Adds the value of self to other.

• #+(other : Number) : Complex

  Adds the value of self to 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 self by other.

• #/(other : Number) : Complex

  Divides self by other.

• #==(other : Complex)

  Determines whether self equals other or not.

• #==(other : Number)

  Determines whether self equals other or not.

• #==(other)

  Determines whether self equals 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)

  See Object#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)

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

• #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 : Float32

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

• #to_f64 : Float64

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

• #to_i

  See #to_i32.

• #to_i16(*args, **options)
• #to_i16(*args, **options, &)
• #to_i32(*args, **options)
• #to_i32(*args, **options, &)
• #to_i64 : Int64

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

• #to_i8(*args, **options)
• #to_i8(*args, **options, &)
• #to_s(io : IO) : Nil

  Writes this complex object to an io.

• #to_u16(*args, **options)
• #to_u16(*args, **options, &)
• #to_u32(*args, **options)
• #to_u32(*args, **options, &)
• #to_u64 : UInt64

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

• #to_u8(*args, **options)
• #to_u8(*args, **options, &)
• #zero? : Bool

  Returns true if the complex number is zero.

Constructor Detail

Instance Method Detail

require "complex"

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

require "complex"

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

require "complex"

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

require "complex"

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

require "complex"

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

require "complex"

Complex.new(7, -24).sign        # => (0.28 - 0.96i)
Complex.new(1.0 / 0.0, 24).sign # => (1.0 + 0.0i)
Complex.new(-0.0, +0.0).sign    # => (-0.0 + 0.0i)

require "complex"

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

require "complex"

Complex.new(0, 0).zero? # => true
Complex.new(1, 0).zero? # => false
Complex.new(0, 1).zero? # => false