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 - 12.0iDefined in:
complex.crClass Method Summary
- .new(real : Number, imag : Number)
-
.zero : Complex
Returns the number
0in complex form.
Instance Method Summary
-
#*(other : Complex)
Multiplies
selfby other. -
#*(other : Number)
Multiplies
selfby other. -
#+(other : Number)
Adds the value of
selfto other. -
#+(other : Complex)
Adds the value of
selfto other. -
#-
Returns the opposite of self.
-
#-(other : Number)
Removes the value from other to self.
-
#-(other : Complex)
Removes the value from other to self.
-
#/(other : Number)
Divides
selfby other. -
#/(other : 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
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.
-
#imag : Float64
Returns the image part of self.
-
#inspect(io : IO)
Write 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 of self.
- #sign
-
#sqrt
Complex#sqrtwas inspired by the following blog post of Pavel Panchekha on floating point precision. -
#to_s(io : IO)
Write this complex object to an io.
Instance methods inherited from struct Struct
==(other : self) : Bool
==,
hash : Int32
hash,
inspect(io : IO) : Nil
inspect,
pretty_print(pp) : Nil
pretty_print,
to_s(io)
to_s
Instance methods inherited from struct Value
==(other)
==,
dup
dup
Instance methods inherited from class Object
!=(other)
!=,
!~(other)
!~,
==(other)
==,
===(other : JSON::Any)===(other : YAML::Any)
===(other) ===, =~(other) =~, class class, dup dup, hash hash, inspect(io : IO)
inspect inspect, itself itself, not_nil! not_nil!, pretty_inspect(width = 79, newline = "\n", indent = 0) : String pretty_inspect, pretty_print(pp : PrettyPrint) : Nil pretty_print, tap(&block) tap, to_json(io : IO)
to_json to_json, to_pretty_json(indent : String = " ")
to_pretty_json(io : IO, indent : String = " ") to_pretty_json, to_s
to_s(io : IO) to_s, to_yaml(io : IO)
to_yaml to_yaml, try(&block) try
Class methods inherited from class Object
from_json(string_or_io, root : String) : selffrom_json(string_or_io) : self from_json, from_yaml(string_or_io) : self from_yaml
Class Method Detail
Instance Method Detail
Returns the absolute value of this complex number in a number form, using the Pythagorean theorem.
Complex.new(42, 2).abs # => 42.047592083257278
Complex.new(-42, 2).abs # => 42.047592083257278Returns the conjugate of self.
Complex.new(42, 2).conj # => 42.0 - 2.0i
Complex.new(42, -2).conj # => 42.0 + 2.0iCalculates the exp of self.
Complex.new(4, 2).exp # => -22.720847417619233 + 49.645957334580565iWrite this complex object to an io, surrounded by parentheses.
Complex.new(42, 2).inspect # => "(42.0 + 2.0i)"Returns a tuple with the abs value and the phase.
Complex.new(42, 2).polar # => {42.047592083257278, 0.047583103276983396}Complex#sqrt was inspired by the following blog post
of Pavel Panchekha on floating point precision.
Write this complex object to an io.
Complex.new(42, 2).to_s # => "42.0 + 2.0i"