Class: Complex

Relationships & Source Files
Super Chains via Extension / Inclusion / Inheritance
Class Chain: self, ::Numeric
Instance Chain: self, ::Numeric, ::Comparable
Inherits:	Numeric ::Object Numeric Complex
Defined in:	complex.c

Overview

A complex number can be represented as a paired real number with imaginary unit; a+bi. Where a is real part, b is imaginary part and i is imaginary unit. Real a equals complex a+0i mathematically.

Complex object can be created as literal, and also by using Kernel.Complex, .rect, .polar or to_c method.

2+1i                 #=> (2+1i)
Complex(1)           #=> (1+0i)
Complex(2, 3)        #=> (2+3i)
Complex.polar(2, 3)  #=> (-1.9799849932008908+0.2822400161197344i)
3.to_c               #=> (3+0i)

You can also create complex object from floating-point numbers or strings.

Complex(0.3)         #=> (0.3+0i)
Complex('0.3-0.5i')  #=> (0.3-0.5i)
Complex('2/3+3/4i')  #=> ((2/3)+(3/4)*i)
Complex('1@2')       #=> (-0.4161468365471424+0.9092974268256817i)

0.3.to_c             #=> (0.3+0i)
'0.3-0.5i'.to_c      #=> (0.3-0.5i)
'2/3+3/4i'.to_c      #=> ((2/3)+(3/4)*i)
'1@2'.to_c           #=> (-0.4161468365471424+0.9092974268256817i)

A complex object is either an exact or an inexact number.

Complex(1, 1) / 2    #=> ((1/2)+(1/2)*i)
Complex(1, 1) / 2.0  #=> (0.5+0.5i)

Constant Summary

I =

The imaginary unit.

# File 'complex.c', line 2270
```
f_complex_new_bang2(rb_cComplex, ZERO, ONE)
```

Class Method Summary

.polar(abs[, arg]) ⇒ Complex

Returns a complex object which denotes the given polar form.
.rect(real[, imag]) ⇒ Complex (also: .rectangular)

Returns a complex object which denotes the given rectangular form.
.rectangular(real[, imag]) ⇒ Complex

Alias for .rect.

Instance Attribute Summary

#real ⇒ Numeric readonly

Returns the real part.
#real? ⇒ Boolean readonly

Returns false.

::Numeric - Inherited

#integer?	Returns `true` if `num` is an ::Integer (including ::Fixnum and ::Bignum).
#negative?	Returns `true` if `num` is less than 0.
#nonzero?	Returns `self` if `num` is not zero, `nil` otherwise.
#positive?	Returns `true` if `num` is greater than 0.
#real	Returns self.
#real?	Returns `true` if `num` is a Real number.
#zero?	Returns `true` if `num` has a zero value.

Instance Method Summary

#*(numeric) ⇒ Complex

Performs multiplication.
#**(numeric) ⇒ Complex

Performs exponentiation.
#+(numeric) ⇒ Complex

Performs addition.
#-(numeric) ⇒ Complex

Performs subtraction.
#- ⇒ Complex

Returns negation of the value.
#/(numeric) ⇒ Complex

Performs division.
#==(object) ⇒ Boolean

Returns true if cmp equals object numerically.
#abs ⇒ Numeric (also: #magnitude)

Returns the absolute part of its polar form.
#abs2 ⇒ Numeric

Returns square of the absolute value.
#angle ⇒ Float

Alias for #arg.
#arg ⇒ Float (also: #angle, #phase)

Returns the angle part of its polar form.
#conj ⇒ Complex

Alias for #~.
#conjugate ⇒ Complex

Alias for #~.
#denominator ⇒ Integer

Returns the denominator (lcm of both denominator - real and imag).
#fdiv(numeric) ⇒ Complex

Performs division as each part is a float, never returns a float.
#imag ⇒ Numeric (also: #imaginary)

Returns the imaginary part.
#imaginary ⇒ Numeric

Alias for #imag.
#inspect ⇒ String

Returns the value as a string for inspection.
#magnitude ⇒ Numeric

Alias for #abs.
#numerator ⇒ Numeric

Returns the numerator.
#phase ⇒ Float

Alias for #arg.
#polar ⇒ Array

Returns an array; [cmp.abs, cmp.arg].
#quo
#rationalize([eps]) ⇒ Rational

Returns the value as a rational if possible (the imaginary part should be exactly zero).
#rect ⇒ Array (also: #rectangular)

Returns an array; [cmp.real, cmp.imag].
#rectangular ⇒ Array

Alias for #rect.
#to_c ⇒ self

Returns self.
#to_f ⇒ Float

Returns the value as a float if possible (the imaginary part should be exactly zero).
#to_i ⇒ Integer

Returns the value as an integer if possible (the imaginary part should be exactly zero).
#to_r ⇒ Rational

Returns the value as a rational if possible (the imaginary part should be exactly zero).
#to_s ⇒ String

Returns the value as a string.
#conj ⇒ Complex (also: #conjugate, #conj)

Returns the complex conjugate.

::Numeric - Inherited

#%	x.modulo(y) means x-y*(x/y).floor.
#+@	Unary Plus—Returns the receiver's value.
#-@	Unary Minus—Returns the receiver's value, negated.
#<=>	Returns zero if `number` equals `other`, otherwise `nil` is returned if the two values are incomparable.
#abs	Returns the absolute value of `num`.
#abs2	Returns square of self.
#angle	Alias for Numeric#arg.
#arg	Returns 0 if the value is positive, pi otherwise.
#ceil	Returns the smallest possible ::Integer that is greater than or equal to `num`.
#coerce	If a `numeric` is the same type as `num`, returns an array containing `numeric` and `num`.
#conj	Returns self.
#conjugate	Alias for Numeric#conj.
#denominator	Returns the denominator (always positive).
#div	Uses #/ to perform division, then converts the result to an integer.
#divmod	Returns an array containing the quotient and modulus obtained by dividing `num` by `numeric`.
#eql?	Returns `true` if `num` and `numeric` are the same type and have equal values.
#fdiv	Returns float division.
#floor	Returns the largest integer less than or equal to `num`.
#i	Returns the corresponding imaginary number.
#imag	Returns zero.
#imaginary	Alias for Numeric#imag.
#initialize_copy	Numerics are immutable values, which should not be copied.
#magnitude	Alias for Numeric#abs.
#modulo	Alias for Numeric#%.
#numerator	Returns the numerator.
#phase	Alias for Numeric#arg.
#polar	Returns an array; [num.abs, num.arg].
#quo	Returns most exact division (rational for integers, float for floats).
#rect	Returns an array; [num, 0].
#rectangular	Alias for Numeric#rect.
#remainder	x.remainder(y) means x-y*(x/y).truncate.
#round	Rounds `num` to a given precision in decimal digits (default 0 digits).
#singleton_method_added	Trap attempts to add methods to ::Numeric objects.
#step	Invokes the given block with the sequence of numbers starting at `num`, incremented by `step` (defaulted to `1`) on each call.
#to_c	Returns the value as a complex.
#to_int	Invokes the child class's #to_i method to convert `num` to an integer.
#truncate	Returns `num` truncated to an ::Integer.

::Comparable - Included

#<	Compares two objects based on the receiver's `<=>` method, returning true if it returns -1.
#<=	Compares two objects based on the receiver's `<=>` method, returning true if it returns -1 or 0.
#==	Compares two objects based on the receiver's `<=>` method, returning true if it returns 0.
#>	Compares two objects based on the receiver's `<=>` method, returning true if it returns 1.
#>=	Compares two objects based on the receiver's `<=>` method, returning true if it returns 0 or 1.
#between?	Returns `false` if obj `<=>` min is less than zero or if anObject `<=>` max is greater than zero, `true` otherwise.

Class Method Details

.polar(abs[, arg]) ⇒ `Complex`

Returns a complex object which denotes the given polar form.

Complex.polar(3, 0)            #=> (3.0+0.0i)
Complex.polar(3, Math::PI/2)   #=> (1.836909530733566e-16+3.0i)
Complex.polar(3, Math::PI)     #=> (-3.0+3.673819061467132e-16i)
Complex.polar(3, -Math::PI/2)  #=> (1.836909530733566e-16-3.0i)

.rect(real[, imag]) ⇒ `Complex` .rectangular(real[, imag]) ⇒ `Complex`
Also known as: .rectangular

Returns a complex object which denotes the given rectangular form.

Complex.rectangular(1, 2)  #=> (1+2i)

.rect(real[, imag]) ⇒ `Complex` .rectangular(real[, imag]) ⇒ `Complex`

Alias for .rect.

Instance Attribute Details

#real ⇒ Numeric (readonly)

Returns the real part.

Complex(7).real      #=> 7
Complex(9, -4).real  #=> 9

#real? ⇒ `Boolean` (readonly)

Returns false.

Instance Method Details

#*(numeric) ⇒ `Complex`

Performs multiplication.

Complex(2, 3)  * Complex(2, 3)   #=> (-5+12i)
Complex(900)   * Complex(1)      #=> (900+0i)
Complex(-2, 9) * Complex(-9, 2)  #=> (0-85i)
Complex(9, 8)  * 4               #=> (36+32i)
Complex(20, 9) * 9.8             #=> (196.0+88.2i)

#**(numeric) ⇒ `Complex`

Performs exponentiation.

Complex('i') ** 2              #=> (-1+0i)
Complex(-8) ** Rational(1, 3)  #=> (1.0000000000000002+1.7320508075688772i)

#+(numeric) ⇒ `Complex`

Performs addition.

Complex(2, 3)  + Complex(2, 3)   #=> (4+6i)
Complex(900)   + Complex(1)      #=> (901+0i)
Complex(-2, 9) + Complex(-9, 2)  #=> (-11+11i)
Complex(9, 8)  + 4               #=> (13+8i)
Complex(20, 9) + 9.8             #=> (29.8+9i)

#-(numeric) ⇒ `Complex`

Performs subtraction.

Complex(2, 3)  - Complex(2, 3)   #=> (0+0i)
Complex(900)   - Complex(1)      #=> (899+0i)
Complex(-2, 9) - Complex(-9, 2)  #=> (7+7i)
Complex(9, 8)  - 4               #=> (5+8i)
Complex(20, 9) - 9.8             #=> (10.2+9i)

#- ⇒ `Complex`

Returns negation of the value.

-Complex(1, 2)  #=> (-1-2i)

#/(numeric) ⇒ `Complex` #quo(numeric) ⇒ `Complex`

Performs division.

Complex(2, 3)  / Complex(2, 3)   #=> ((1/1)+(0/1)*i)
Complex(900)   / Complex(1)      #=> ((900/1)+(0/1)*i)
Complex(-2, 9) / Complex(-9, 2)  #=> ((36/85)-(77/85)*i)
Complex(9, 8)  / 4               #=> ((9/4)+(2/1)*i)
Complex(20, 9) / 9.8             #=> (2.0408163265306123+0.9183673469387754i)

#==(object) ⇒ `Boolean`

Returns true if cmp equals object numerically.

Complex(2, 3)  == Complex(2, 3)   #=> true
Complex(5)     == 5               #=> true
Complex(0)     == 0.0             #=> true
Complex('1/3') == 0.33            #=> false
Complex('1/2') == '1/2'           #=> false

#abs ⇒ Numeric #magnitude ⇒ Numeric
Also known as: #magnitude

Returns the absolute part of its polar form.

Complex(-1).abs         #=> 1
Complex(3.0, -4.0).abs  #=> 5.0

#abs2 ⇒ Numeric

Returns square of the absolute value.

Complex(-1).abs2         #=> 1
Complex(3.0, -4.0).abs2  #=> 25.0

#arg ⇒ Float #angle ⇒ Float #phase ⇒ Float

Alias for #arg.

#arg ⇒ Float #angle ⇒ Float #phase ⇒ Float
Also known as: #angle, #phase

Returns the angle part of its polar form.

Complex.polar(3, Math::PI/2).arg  #=> 1.5707963267948966

#conj ⇒ `Complex` #conjugate ⇒ `Complex`

Alias for #~.

#conj ⇒ `Complex` #conjugate ⇒ `Complex`

Alias for #~.

#denominator ⇒ Integer

Returns the denominator (lcm of both denominator - real and imag).

See numerator.

#fdiv(numeric) ⇒ `Complex`

Performs division as each part is a float, never returns a float.

Complex(11, 22).fdiv(3)  #=> (3.6666666666666665+7.333333333333333i)

#imag ⇒ Numeric #imaginary ⇒ Numeric
Also known as: #imaginary

Returns the imaginary part.

Complex(7).imaginary      #=> 0
Complex(9, -4).imaginary  #=> -4

#imag ⇒ Numeric #imaginary ⇒ Numeric

Alias for #imag.

#inspect ⇒ String

Returns the value as a string for inspection.

Complex(2).inspect                       #=> "(2+0i)"
Complex('-8/6').inspect                  #=> "((-4/3)+0i)"
Complex('1/2i').inspect                  #=> "(0+(1/2)*i)"
Complex(0, Float::INFINITY).inspect      #=> "(0+Infinity*i)"
Complex(Float::NAN, Float::NAN).inspect  #=> "(NaN+NaN*i)"

#abs ⇒ Numeric #magnitude ⇒ Numeric

Alias for #abs.

#numerator ⇒ Numeric

Returns the numerator.

1   2       3+4i  <-  numerator
    - + -i  ->  ----
    2   3        6    <-  denominator

c = Complex('1/2+2/3i')  #=> ((1/2)+(2/3)*i)
n = c.numerator          #=> (3+4i)
d = c.denominator        #=> 6
n / d                    #=> ((1/2)+(2/3)*i)
Complex(Rational(n.real, d), Rational(n.imag, d))
                         #=> ((1/2)+(2/3)*i)

See denominator.

#arg ⇒ Float #angle ⇒ Float #phase ⇒ Float

Alias for #arg.

#polar ⇒ Array

Returns an array; [cmp.abs, cmp.arg].

Complex(1, 2).polar  #=> [2.23606797749979, 1.1071487177940904]

#quo

#rationalize([eps]) ⇒ Rational

Returns the value as a rational if possible (the imaginary part should be exactly zero).

Complex(1.0/3, 0).rationalize  #=> (1/3)
Complex(1, 0.0).rationalize    # RangeError
Complex(1, 2).rationalize      # RangeError

See to_r.

#rect ⇒ Array #rectangular ⇒ Array
Also known as: #rectangular

Returns an array; [cmp.real, cmp.imag].

Complex(1, 2).rectangular  #=> [1, 2]

#rect ⇒ Array #rectangular ⇒ Array

Alias for #rect.

#to_c ⇒ `self`

Returns self.

Complex(2).to_c      #=> (2+0i)
Complex(-8, 6).to_c  #=> (-8+6i)

#to_f ⇒ Float

Returns the value as a float if possible (the imaginary part should be exactly zero).

Complex(1, 0).to_f    #=> 1.0
Complex(1, 0.0).to_f  # RangeError
Complex(1, 2).to_f    # RangeError

#to_i ⇒ Integer

Returns the value as an integer if possible (the imaginary part should be exactly zero).

Complex(1, 0).to_i    #=> 1
Complex(1, 0.0).to_i  # RangeError
Complex(1, 2).to_i    # RangeError

#to_r ⇒ Rational

Returns the value as a rational if possible (the imaginary part should be exactly zero).

Complex(1, 0).to_r    #=> (1/1)
Complex(1, 0.0).to_r  # RangeError
Complex(1, 2).to_r    # RangeError

See rationalize.

#to_s ⇒ String

Returns the value as a string.

Complex(2).to_s                       #=> "2+0i"
Complex('-8/6').to_s                  #=> "-4/3+0i"
Complex('1/2i').to_s                  #=> "0+1/2i"
Complex(0, Float::INFINITY).to_s      #=> "0+Infinity*i"
Complex(Float::NAN, Float::NAN).to_s  #=> "NaN+NaN*i"

#conj ⇒ `Complex` #conjugate ⇒ `Complex`
Also known as: #conjugate, #conj

Returns the complex conjugate.

Complex(1, 2).conjugate  #=> (1-2i)

Class: Complex

Overview

Constant Summary

Class Method Summary

Instance Attribute Summary

::Numeric - Inherited

Instance Method Summary

::Numeric - Inherited

::Comparable - Included

Class Method Details

.polar(abs[, arg]) ⇒ Complex

.rect(real[, imag]) ⇒ Complex .rectangular(real[, imag]) ⇒ Complex Also known as: .rectangular

.rect(real[, imag]) ⇒ Complex .rectangular(real[, imag]) ⇒ Complex

Instance Attribute Details

#real ⇒ Numeric (readonly)

#real? ⇒ Boolean (readonly)

Instance Method Details

#*(numeric) ⇒ Complex

#**(numeric) ⇒ Complex

#+(numeric) ⇒ Complex

#-(numeric) ⇒ Complex

#- ⇒ Complex

#/(numeric) ⇒ Complex #quo(numeric) ⇒ Complex

#==(object) ⇒ Boolean

#abs ⇒ Numeric #magnitude ⇒ Numeric Also known as: #magnitude

#abs2 ⇒ Numeric

#arg ⇒ Float #angle ⇒ Float #phase ⇒ Float

#arg ⇒ Float #angle ⇒ Float #phase ⇒ Float Also known as: #angle, #phase

#conj ⇒ Complex #conjugate ⇒ Complex

#conj ⇒ Complex #conjugate ⇒ Complex

#denominator ⇒ Integer

#fdiv(numeric) ⇒ Complex

#imag ⇒ Numeric #imaginary ⇒ Numeric Also known as: #imaginary

#imag ⇒ Numeric #imaginary ⇒ Numeric

#inspect ⇒ String

#abs ⇒ Numeric #magnitude ⇒ Numeric

#numerator ⇒ Numeric

#arg ⇒ Float #angle ⇒ Float #phase ⇒ Float

#polar ⇒ Array

#quo

#rationalize([eps]) ⇒ Rational

#rect ⇒ Array #rectangular ⇒ Array Also known as: #rectangular

#rect ⇒ Array #rectangular ⇒ Array

#to_c ⇒ self

#to_f ⇒ Float

#to_i ⇒ Integer

#to_r ⇒ Rational

#to_s ⇒ String

#conj ⇒ Complex #conjugate ⇒ Complex Also known as: #conjugate, #conj

.polar(abs[, arg]) ⇒ `Complex`

.rect(real[, imag]) ⇒ `Complex` .rectangular(real[, imag]) ⇒ `Complex`
Also known as: .rectangular

.rect(real[, imag]) ⇒ `Complex` .rectangular(real[, imag]) ⇒ `Complex`

#real? ⇒ `Boolean` (readonly)

#*(numeric) ⇒ `Complex`

#**(numeric) ⇒ `Complex`

#+(numeric) ⇒ `Complex`

#-(numeric) ⇒ `Complex`

#- ⇒ `Complex`

#/(numeric) ⇒ `Complex` #quo(numeric) ⇒ `Complex`

#==(object) ⇒ `Boolean`

#abs ⇒ Numeric #magnitude ⇒ Numeric
Also known as: #magnitude

#arg ⇒ Float #angle ⇒ Float #phase ⇒ Float
Also known as: #angle, #phase

#conj ⇒ `Complex` #conjugate ⇒ `Complex`

#conj ⇒ `Complex` #conjugate ⇒ `Complex`

#fdiv(numeric) ⇒ `Complex`

#imag ⇒ Numeric #imaginary ⇒ Numeric
Also known as: #imaginary

#rect ⇒ Array #rectangular ⇒ Array
Also known as: #rectangular

#to_c ⇒ `self`

#conj ⇒ `Complex` #conjugate ⇒ `Complex`
Also known as: #conjugate, #conj