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.

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

Defined in:

complex.cr

Class Method Summary

Instance Method Summary

Instance methods inherited from struct Struct

==(other : self) : Bool ==, hash : Int32 hash, inspect(io : IO) : Nil inspect, to_s(io) to_s

Instance methods inherited from struct Value

==(other) ==, dup dup

Instance methods inherited from class Object

!=(other) !=, !~(other) !~, ==(other) ==, ===(other)
===(other : YAML::Any)
===(other : JSON::Any) ===, =~(other) =~, class class, crystal_type_id crystal_type_id, dup dup, hash hash, inspect(io : IO)
inspect inspect, itself itself, not_nil! not_nil!, tap(&block) tap, to_json to_json, to_pretty_json(io : IO)
to_pretty_json to_pretty_json, to_s
to_s(io : IO) to_s, to_yaml
to_yaml(io : IO) to_yaml, try(&block) try

Class methods inherited from class Object

==(other : Class) ==, ===(other) ===, cast(other) : self cast, clone clone, dup dup, from_json(string_or_io, root : String) : self
from_json(string_or_io) : self from_json, from_yaml(string : String) : self from_yaml, hash hash, inspect(io) inspect, name : String name, to_s(io) to_s, |(other : U.class) |

Class Method Detail

def self.zero : Complex #

Returns the number 0 in complex form


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

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Instance Method Detail

def *(other : Number) #

Multiplies self by other


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def *(other : Complex) #

Multiplies self by other


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def +(other : Number) #

Adds the value of self to other


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def +(other : Complex) #

Adds the value of self to other


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def -(other : Number) #

Removes the value from other to self


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def - #

 Returns the opposite of self


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def -(other : Complex) #

Removes the value from other to self


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def /(other : Complex) #

Divides self by other


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def /(other : Number) #

 ditto


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def ==(other : Number) #

Determines whether self equals other or not


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def ==(other) #

Determines whether self equals other or not


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def ==(other : Complex) #

Determines whether self equals other or not


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def abs #

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

Complex.new(42, 2).abs  # => 42.0476
Complex.new(-42, 2).abs # => 42.0476

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def abs2 #

Returns the square of absolute value in a number form.

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

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def clone #

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def conj #

Returns the conjugate of self

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

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def exp #

Calculates the exp of self

Complex.new(4, 2).exp #  => -22.7208 + 49.646i

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def imag : Float64 #

Returns the image part of self


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def inspect(io : IO) #

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

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

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def inv #

Returns the inverse of self


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def log #

Calculates the log of self


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def log10 #

Calculates the log10 of self


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def log2 #

Calculates the log2 of self


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def phase #

Returns the phase of self


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def polar #

Returns a tuple with the abs value and the phase.

Complex.new(42, 2).polar # => {2.54311, 0.665774}

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def real : Float64 #

 Returns the real part of self


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def sign #

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def sqrt #

Complex.sqrt was inspired by the following blog post of Pavel Panchekha on floating point precision: https://pavpanchekha.com/casio/index.html


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def to_s(io : IO) #

Write this complex object to an io

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

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