# 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

## Instance Method Summary

• #*(other : Number)

Multiplies `self` by other.

• #*(other : Complex)

Multiplies `self` by other.

• #+(other : Complex)

Adds the value of `self` to other.

• #+(other : Number)

Adds the value of `self` to other.

• #+

Returns absolute value of `self`.

• #-

Returns the opposite of `self`.

• #-(other : Number)

Removes the value of other from `self`.

• #-(other : Complex)

Removes the value of other from `self`.

• #/(other : Number)

Divides `self` by other.

• #/(other : 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

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

• #abs2

Returns the square of absolute value in a number form.

• #clone
• #conj

Returns the conjugate of `self`.

• #exp

Calculates the exp of `self`.

• #hash(hasher)

See `Object#hash(hasher)`

• #imag : Float64

Returns the imaginary part.

• #inspect(io : IO)

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

• #inv

Returns the inverse of `self`.

• #log

Calculates the log of `self`.

• #log10

Calculates the log10 of `self`.

• #log2

Calculates the log2 of `self`.

• #phase

Returns the phase of `self`.

• #polar

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

• #real : Float64

Returns the real part.

• #sign
• #sqrt

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

• #to_c

Returns `self`.

• #to_f

See `#to_f64`.

• #to_f32

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

• #to_f64

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

• #to_i

See `#to_i32`.

• #to_i32

Returns the value as a `Int32` if possible (the imaginary part should be exactly zero), raises otherwise.

• #to_i64

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

• #to_s(io : IO)

Writes this complex object to an io.

• #zero? : Bool

, , , ,

,

### Instance methods inherited from class `Object`

, , , , , , , , , , , , , , , , , , ,

,

## Constructor Detail

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

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 - #

Returns the opposite of `self`.

def -(other : Number) #

Removes the value of other from `self`.

def -(other : Complex) #

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.

``````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.

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

def clone #

def conj #

Returns the conjugate of `self`.

``````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`.

``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) #

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

``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`.

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

def real : Float64 #

Returns the real part.

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_i32 #

Returns the value as a `Int32` if possible (the imaginary part should be exactly zero), raises otherwise.

def to_i64 #

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

def to_s(io : IO) #

Writes this complex object to an io.

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

def zero? : Bool #