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``````

complex.cr

Constructor Detail

def self.new(real : Number, imag : Number = 0) #

def self.new(c : Complex) #

def self.zero : Complex #

Returns the number `0` in complex form.

Instance Method Detail

def *(other : Number) #

Multiplies `self` by other.

def *(other : Complex) #

Multiplies `self` by other.

def +(other : Complex) #

Adds the value of `self` to other.

def +(other : Number) #

Adds the value of `self` to other.

def + #

Returns absolute value of `self`.

def -(other : Complex) #

Removes the value of other from `self`.

def - #

Returns the opposite of `self`.

def -(other : Number) #

Removes the value of other from `self`.

def /(other : Number) #

Divides `self` by other.

def /(other : Complex) #

Divides `self` by other.

def ==(other : Complex) #

Determines whether `self` equals other or not.

def ==(other : Number) #

Determines whether `self` equals other or not.

def ==(other) #

Determines whether `self` equals other or not.

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``````

def abs2 #

Returns the square of absolute value in a number form.

``````require "complex"

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

def clone #

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``````

def exp #

Calculates the exp of `self`.

``````require "complex"

Complex.new(4, 2).exp # => -22.720847417619233 + 49.645957334580565i``````

def hash(hasher) #

See `Object#hash(hasher)`

def imag : Float64 #

Returns the imaginary part.

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)"``````

def inv #

Returns the inverse of `self`.

def log #

Calculates the log of `self`.

def log10 #

Calculates the log10 of `self`.

def log2 #

Calculates the log2 of `self`.

def phase #

Returns the phase of `self`.

def polar #

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

``````require "complex"

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

def real : Float64 #

Returns the real part.

def round(digits = 0) #

Rounds to the nearest digits.

def sign #

def sqrt #

`Complex#sqrt` was inspired by the following blog post of Pavel Panchekha on floating point precision.

def to_c #

Returns `self`.

def to_f #

See `#to_f64`.

def to_f32 #

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

def to_f64 #

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

def to_i #

See `#to_i32`.

def to_i16(*args, **options) #

def to_i16(*args, **options, &) #

def to_i32(*args, **options) #

def to_i32(*args, **options, &) #

def to_i64 #

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

def to_i8(*args, **options) #

def to_i8(*args, **options, &) #

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"``````

def to_u16(*args, **options) #

def to_u16(*args, **options, &) #

def to_u32(*args, **options) #

def to_u32(*args, **options, &) #

def to_u64 #

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

def to_u8(*args, **options) #

def to_u8(*args, **options, &) #

def zero? : Bool #