Class

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.

You can create a Complex object explicitly with:

You can convert certain objects to Complex objects with:

Complex object can be created as literal, and also by using Kernel#Complex, Complex::rect, Complex::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)
Constants

The imaginary unit.

Class Methods

Deserializes JSON string by converting Real value r, imaginary value i, to a Complex object.

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)

Returns a complex object which denotes the given rectangular form.

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

Returns a complex object which denotes the given rectangular form.

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

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)

Performs exponentiation.

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

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)

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)

Returns negation of the value.

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

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)

If cmp‘s imaginary part is zero, and object is also a real number (or a Complex number where the imaginary part is zero), compare the real part of cmp to object. Otherwise, return nil.

Complex(2, 3)  <=> Complex(2, 3)   #=> nil
Complex(2, 3)  <=> 1               #=> nil
Complex(2)     <=> 1               #=> 1
Complex(2)     <=> 2               #=> 0
Complex(2)     <=> 3               #=> -1

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

Returns the absolute part of its polar form.

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

Returns square of the absolute value.

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

Returns the angle part of its polar form.

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

Returns a hash, that will be turned into a JSON object and represent this object.

Returns the complex conjugate.

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

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

See numerator.

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

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

Returns true if cmp‘s real and imaginary parts are both finite numbers, otherwise returns false.

No documentation available

Returns the imaginary part.

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

Returns 1 if cmp‘s real or imaginary part is an infinite number, otherwise returns nil.

For example:

   (1+1i).infinite?                   #=> nil
   (Float::INFINITY + 1i).infinite?   #=> 1

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)"

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.

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

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

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)

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.

Returns the real part.

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

Returns false, even if the complex number has no imaginary part.

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

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

Returns self.

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

Returns the value as a BigDecimal.

The precision parameter is required for a rational complex number. This parameter is used to determine the number of significant digits for the result.

require 'bigdecimal'
require 'bigdecimal/util'

Complex(0.1234567, 0).to_d(4)   # => 0.1235e0
Complex(Rational(22, 7), 0).to_d(3)   # => 0.314e1

See also BigDecimal::new.

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

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

Stores class name (Complex) along with real value r and imaginary value i as JSON string

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.

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"