class Complex

A Complex object houses a pair of values, given when the object is created as either rectangular coordinates or polar coordinates.

Rectangular Coordinates¶ ↑

The rectangular coordinates of a complex number are called the real and imaginary parts; see Complex number definition.

You can create a Complex object from rectangular coordinates with:

A complex literal.
Method Complex.rect.
Method Kernel#Complex, either with numeric arguments or with certain string arguments.
Method String#to_c, for certain strings.

Note that each of the stored parts may be a an instance one of the classes Complex, Float, Integer, or Rational; they may be retrieved:

Separately, with methods Complex#real and Complex#imaginary.
Together, with method Complex#rect.

The corresponding (computed) polar values may be retrieved:

Separately, with methods Complex#abs and Complex#arg.
Together, with method Complex#polar.

Polar Coordinates¶ ↑

The polar coordinates of a complex number are called the absolute and argument parts; see Complex polar plane.

In this class, the argument part in expressed radians (not degrees).

You can create a Complex object from polar coordinates with:

Method Complex.polar.
Method Kernel#Complex, with certain string arguments.
Method String#to_c, for certain strings.

Note that each of the stored parts may be a an instance one of the classes Complex, Float, Integer, or Rational; they may be retrieved:

Separately, with methods Complex#abs and Complex#arg.
Together, with method Complex#polar.

The corresponding (computed) rectangular values may be retrieved:

Separately, with methods Complex#real and Complex#imag.
Together, with method Complex#rect.

Constants

I

Equivalent to Complex(0, 1):

Complex::I # => (0+1i)

Public Class Methods

polar(abs, arg = 0) → complex click to toggle source

Returns a new Complex object formed from the arguments, each of which must be an instance of Numeric, or an instance of one of its subclasses: Complex, Float, Integer, Rational. Argument arg is given in radians; see Polar Coordinates:

Complex.polar(3)        # => (3+0i)
Complex.polar(3, 2.0)   # => (-1.2484405096414273+2.727892280477045i)
Complex.polar(-3, -2.0) # => (1.2484405096414273+2.727892280477045i)

static VALUE
nucomp_s_polar(int argc, VALUE *argv, VALUE klass)
{
    VALUE abs, arg;

    argc = rb_scan_args(argc, argv, "11", &abs, &arg);
    abs = nucomp_real_check(abs);
    if (argc == 2) {
        arg = nucomp_real_check(arg);
    }
    else {
        arg = ZERO;
    }
    return f_complex_polar_real(klass, abs, arg);
}

rect(real, imag = 0) → complex click to toggle source

Complex.rect(3)             # => (3+0i)
Complex.rect(3, Math::PI)   # => (3+3.141592653589793i)
Complex.rect(-3, -Math::PI) # => (-3-3.141592653589793i)

Complex.rectangular is an alias for Complex.rect.

static VALUE
nucomp_s_new(int argc, VALUE *argv, VALUE klass)
{
    VALUE real, imag;

    switch (rb_scan_args(argc, argv, "11", &real, &imag)) {
      case 1:
        real = nucomp_real_check(real);
        imag = ZERO;
        break;
      default:
        real = nucomp_real_check(real);
        imag = nucomp_real_check(imag);
        break;
    }

    return nucomp_s_new_internal(klass, real, imag);
}

rect(real, imag = 0) → complex click to toggle source

Complex.rect(3)             # => (3+0i)
Complex.rect(3, Math::PI)   # => (3+3.141592653589793i)
Complex.rect(-3, -Math::PI) # => (-3-3.141592653589793i)

Complex.rectangular is an alias for Complex.rect.

static VALUE
nucomp_s_new(int argc, VALUE *argv, VALUE klass)
{
    VALUE real, imag;

    switch (rb_scan_args(argc, argv, "11", &real, &imag)) {
      case 1:
        real = nucomp_real_check(real);
        imag = ZERO;
        break;
      default:
        real = nucomp_real_check(real);
        imag = nucomp_real_check(imag);
        break;
    }

    return nucomp_s_new_internal(klass, real, imag);
}

Public Instance Methods

complex * numeric → new_complex click to toggle source

Returns the product of self and numeric:

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)  *