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.

What’s Here

First, what’s elsewhere:

Class Complex inherits (directly or indirectly) from classes Numeric and Object.
Includes (indirectly) module Comparable.

Here, class Complex has methods for:

Creating Complex Objects

::polar: Returns a new Complex object based on given polar coordinates.
::rect (and its alias ::rectangular): Returns a new Complex object based on given rectangular coordinates.

Querying

abs (and its alias magnitude): Returns the absolute value for self.
arg (and its aliases angle and phase): Returns the argument (angle) for self in radians.
denominator: Returns the denominator of self.
finite?: Returns whether both self.real and self.image are finite.
hash: Returns the integer hash value for self.
imag (and its alias imaginary): Returns the imaginary value for self.
infinite?: Returns whether self.real or self.image is infinite.
numerator: Returns the numerator of self.
polar: Returns the array [self.abs, self.arg].
inspect: Returns a string representation of self.
real: Returns the real value for self.
real?: Returns false; for compatibility with Numeric#real?.
rect (and its alias rectangular): Returns the array [self.real, self.imag].

Comparing

<=>: Returns whether self is less than, equal to, or greater than the given argument.
==: Returns whether self is equal to the given argument.

Converting

rationalize: Returns a Rational object whose value is exactly or approximately equivalent to that of self.real.
to_c: Returns self.
to_d: Returns the value as a BigDecimal object.
to_f: Returns the value of self.real as a Float, if possible.
to_i: Returns the value of self.real as an Integer, if possible.
to_r: Returns the value of self.real as a Rational, if possible.
to_s: Returns a string representation of self.

Performing `Complex` Arithmetic

*: Returns the product of self and the given numeric.
**: Returns self raised to power of the given numeric.
+: Returns the sum of self and the given numeric.
-: Returns the difference of self and the given numeric.
-@: Returns the negation of self.
/: Returns the quotient of self and the given numeric.
abs2: Returns square of the absolute value (magnitude) for self.
conj (and its alias conjugate): Returns the conjugate of self.
fdiv: Returns Complex.rect(self.real/numeric, self.imag/numeric).

Working with `JSON`

::json_create: Returns a new Complex object, deserialized from the given serialized hash.
as_json: Returns a serialized hash constructed from self.
to_json: Returns a JSON string representing self.

These methods are provided by the JSON gem. To make these methods available:

require 'json/add/complex'

Constants

I

Equivalent to Complex.rect(0, 1):

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

Public Class Methods

json_create (object)

Source

# File ext/json/lib/json/add/complex.rb, line 9
def self.json_create(object)
  Complex(object['r'], object['i'])
end

See as_json.

polar(abs, arg = 0) → complex

Source

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);
}

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)

rect(real, imag = 0) → complex

Source

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);
}

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.

rect(real, imag = 0) → complex

Source

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);
}

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.

Public Instance Methods

self * other → numeric

Source

VALUE
rb_complex_mul(VALUE self, VALUE other)
{
    if (RB_TYPE_P(other, T_COMPLEX)) {
        VALUE real, imag;
        get_dat2(self, other);

        comp_mul(adat->real, adat->imag, bdat->real, bdat->imag, &real, &imag);

        return f_complex_new2(CLASS_OF(self), real, imag);
    }
    if (k_numeric_p(other) && f_real_p(other)) {
        get_dat1(self);

        return f_complex_new2(CLASS_OF(self),
                              f_mul(dat->real, other),
                              f_mul(dat->imag, other));
    }
    return rb_num_coerce_bin(self, other, '*');
}

Returns the numeric product of self and other:

Complex.rect(9, 8)  * 4                   # => (36+32i)
Complex.rect(20, 9) * 9.8                 # => (196.0+88.2i)
Complex.rect(2, 3)  * Complex.rect(2, 3)  # => (-5+12i)
Complex.rect(900)   * Complex.rect(1)     # => (900+0i)
Complex.rect(-2, 9) * Complex.rect(-9, 2) # => (0-85i)
Complex.rect(9, 8)  * Rational(2, 3)      # => ((6/1)+(16/3)*i)

self ** exponent → complex

Source

VALUE
rb_complex_pow(VALUE self, VALUE other)
{
    if (k_numeric_p(other) && k_exact_zero_p(other))
        return f_complex_new_bang1(CLASS_OF(self), ONE);

    if (RB_TYPE_P(other, T_RATIONAL) && RRATIONAL(other)->den == LONG2FIX(1))
        other = RRATIONAL(other)->num; /* c14n */

    if (RB_TYPE_P(other, T_COMPLEX)) {
        get_dat1(other);

        if (k_exact_zero_p(dat->imag))
            other = dat->real; /* c14n */
    }

    if (other == ONE) {
        get_dat1(self);
        return nucomp_s_new_internal(CLASS_OF(self), dat->real, dat->imag);
    }

    VALUE result = complex_pow_for_special_angle(self, other);
    if (!UNDEF_P(result)) return result;

    if (RB_TYPE_P(other, T_COMPLEX)) {
        VALUE r, theta, nr, ntheta;

        get_dat1(other);

        r = f_abs(self);
        theta = f_arg(self);

        nr = m_exp_bang(f_sub(f_mul(dat->real, m_log_bang(r)),
                              f_mul(dat->imag, theta)));
        ntheta = f_add(f_mul(theta, dat->real),
                       f_mul(dat->imag, m_log_bang(r)));
        return f_complex_polar(CLASS_OF(self), nr, ntheta);
    }
    if (FIXNUM_P(other)) {
        long n = FIX2LONG(other);
        if (n == 0) {
            return nucomp_s_new_internal(CLASS_OF(self), ONE, ZERO);
        }
        if (n < 0) {
            self = f_reciprocal(self);
            other = rb_int_uminus(other);
            n = -n;
        }
        {
            get_dat1(self);
            VALUE xr = dat->real, xi = dat->imag, zr = xr, zi = xi;

            if (f_zero_p(xi)) {
                zr = rb_num_pow(zr, other);
            }
            else if (f_zero_p(xr)) {
                zi = rb_num_pow(zi, other);
                if (n & 2) zi = f_negate(zi);
                if (!(n & 1)) {
                    VALUE tmp = zr;
                    zr = zi;
                    zi = tmp;
                }
            }
            else {
                while (--n) {
                    long q, r;

                    for (; q = n / 2, r = n % 2, r == 0; n = q) {
                        VALUE tmp = f_sub(f_mul(xr, xr), f_mul(xi, xi));
                        xi = f_mul(f_mul(TWO, xr), xi);
                        xr = tmp;
                    }
                    comp_mul(zr, zi, xr, xi, &zr, &zi);
                }
            }
            return nucomp_s_new_internal(CLASS_OF(self), zr, zi);
        }
    }
    if (k_numeric_p(other) && f_real_p(other)) {
        VALUE r, theta;

        if (RB_BIGNUM_TYPE_P(other))
            rb_warn("in a**b, b may be too big");

        r = f_abs(self);
        theta = f_arg(self);

        return f_complex_polar(CLASS_OF(self), f_expt(r, other),
                               f_mul(theta, other));
    }
    return rb_num_coerce_bin(self, other, id_expt);
}

Returns self raised to the power exponent:

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

self + other → numeric

Source

VALUE
rb_complex_plus(VALUE self, VALUE other)
{
    if (RB_TYPE_P(other, T_COMPLEX)) {
        VALUE real, imag;

        get_dat2(self, other);

        real = f_add(adat->real, bdat->real);
        imag = f_add(adat->imag, bdat->imag);

        return f_complex_new2(CLASS_OF(self), real, imag);
    }
    if (k_numeric_p(other) && f_real_p(other)) {
        get_dat1(self);

        return f_complex_new2(CLASS_OF(self),
                              f_add(dat->real, other), dat->imag);
    }
    return rb_num_coerce_bin(self, other, '+');
}

Returns the sum of self and other:

Complex(1, 2) + 0  # => (1+2i)
Complex(1, 2) + 1  # => (2+2i)
Complex(1, 2) + -1 # => (0+2i)

Complex(1, 2) + 1.0  # => (2.0+2i)

Complex(1, 2) + Complex(2, 1)     # => (3+3i)
Complex(1, 2) + Complex(2.0, 1.0) # => (3.0+3.0i)

Complex(1, 2) + Rational(1, 1) # => ((2/1)+2i)
Complex(1, 2) + Rational(1, 2) # => ((3/2)+2i)

For a computation involving Floats, the result may be inexact (see Float#+):

Complex(1, 2) + 3.14 # => (4.140000000000001+2i)

self - other → complex

Source

VALUE
rb_complex_minus(VALUE self, VALUE other)
{
    if (RB_TYPE_P(other, T_COMPLEX)) {
        VALUE real, imag;

        get_dat2(self, other);

        real = f_sub(adat->real, bdat->real);
        imag = f_sub(adat->imag, bdat->imag);

        return f_complex_new2(CLASS_OF(self), real, imag);
    }
    if (k_numeric_p(other) && f_real_p(other)) {
        get_dat1(self);

        return f_complex_new2(CLASS_OF(self),
                              f_sub(dat->real, other), dat->imag);
    }
    return rb_num_coerce_bin(self, other, '-');
}

Returns the difference of self and other:

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

-self → complex

Source

VALUE
rb_complex_uminus(VALUE self)
{
    get_dat1(self);
    return f_complex_new2(CLASS_OF(self),
                          f_negate(dat->real), f_negate(dat->imag));
}

Returns self, negated, which is the negation of each of its parts:

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

self / other → complex

Source

VALUE
rb_complex_div(VALUE self, VALUE other)
{
    return f_divide(self, other, f_quo, id_quo);
}

Returns the quotient of self and other:

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

self <=> other → -1, 0, 1, or nil

Source

static VALUE
nucomp_cmp(VALUE self, VALUE other)
{
    if (!k_numeric_p(other)) {
        return rb_num_coerce_cmp(self, other, idCmp);
    }
    if (!nucomp_real_p(self)) {
        return Qnil;
    }
    if (RB_TYPE_P(other, T_COMPLEX)) {
        if (nucomp_real_p(other)) {
            get_dat2(self, other);
            return rb_funcall(adat->real, idCmp, 1, bdat->real);
        }
    }
    else {
        get_dat1(self);
        if (f_real_p(other)) {
            return rb_funcall(dat->real, idCmp, 1, other);
        }
        else {
            return rb_num_coerce_cmp(dat->real, other, idCmp);
        }
    }
    return Qnil;
}

Compares self and other.

Returns:

self.real <=> other.real if both of the following are true:
- self.imag == 0.
- other.imag == 0 (always true if other is numeric but not complex).
nil otherwise.

Examples:

Complex.rect(2) <=> 3                  # => -1
Complex.rect(2) <=> 2                  # => 0
Complex.rect(2) <=> 1                  # => 1
Complex.rect(2, 1) <=> 1               # => nil # self.imag not zero.
Complex.rect(1) <=> Complex.rect(1, 1) # => nil # object.imag not zero.
Complex.rect(1) <=> 'Foo'              # => nil # object.imag not defined.

Class Complex includes module Comparable, each of whose methods uses Complex#<=> for comparison.

complex == object → true or false

Source

static VALUE
nucomp_eqeq_p(VALUE self, VALUE other)
{
    if (RB_TYPE_P(other, T_COMPLEX)) {
        get_dat2(self, other);

        return RBOOL(f_eqeq_p(adat->real, bdat->real) &&
                          f_eqeq_p(adat->imag, bdat->imag));
    }
    if (k_numeric_p(other) && f_real_p(other)) {
        get_dat1(self);

        return RBOOL(f_eqeq_p(dat->real, other) && f_zero_p(dat->imag));
    }
    return RBOOL(f_eqeq_p(other, self));
}

Returns true if self.real == object.real and self.imag == object.imag:

Complex.rect(2, 3)  == Complex.rect(2.0, 3.0) # => true

abs → float

Source

VALUE
rb_complex_abs(VALUE self)
{
    get_dat1(self);

    if (f_zero_p(dat->real)) {
        VALUE a = f_abs(dat->imag);
        if (RB_FLOAT_TYPE_P(dat->real) && !RB_FLOAT_TYPE_P(dat->imag))
            a = f_to_f(a);
        return a;
    }
    if (f_zero_p(dat->imag)) {
        VALUE a = f_abs(dat->real);
        if (!RB_FLOAT_TYPE_P(dat->real) && RB_FLOAT_TYPE_P(dat->imag))
            a = f_to_f(a);
        return a;
    }
    return rb_math_hypot(dat->real, dat->imag);
}

Returns the absolute value (magnitude) for self; see polar coordinates:

Complex.polar(-1, 0).abs # => 1.0

If self was created with rectangular coordinates, the returned value is computed, and may be inexact:

Complex.rectangular(1, 1).abs # => 1.4142135623730951 # The square root of 2.

Also aliased as: magnitude

abs2 → float

Source

static VALUE
nucomp_abs2(VALUE self)
{
    get_dat1(self);
    return f_add(f_mul(dat->real, dat->real),
                 f_mul(dat->imag, dat->imag));
}

Returns square of the absolute value (magnitude) for self; see polar coordinates:

Complex.polar(2, 2).abs2 # => 4.0

If self was created with rectangular coordinates, the returned value is computed, and may be inexact:

Complex.rectangular(1.0/3, 1.0/3).abs2 # => 0.2222222222222222

angle

Alias for: arg

arg → float

Source

VALUE
rb_complex_arg(VALUE self)
{
    get_dat1(self);
    return rb_math_atan2(dat->imag, dat->real);
}

Returns the argument (angle) for self in radians; see polar coordinates:

Complex.polar(3, Math::PI/2).arg  # => 1.57079632679489660

If self was created with rectangular coordinates, the returned value is computed, and may be inexact:

Complex.polar(1, 1.0/3).arg # => 0.33333333333333326

Also aliased as: angle, phase

as_json (*)

Source

# File ext/json/lib/json/add/complex.rb, line 29
def as_json(*)
  {
    JSON.create_id => self.class.name,
    'r'            => real,
    'i'            => imag,
  }
end

Methods Complex#as_json and Complex.json_create may be used to serialize and deserialize a Complex object; see Marshal.

Method Complex#as_json serializes self, returning a 2-element hash representing self:

require 'json/add/complex'
x = Complex(2).as_json      # => {"json_class"=>"Complex", "r"=>2, "i"=>0}
y = Complex(2.0, 4).as_json # => {"json_class"=>"Complex", "r"=>2.0, "i"=>4}

Method JSON.create deserializes such a hash, returning a Complex object:

Complex.json_create(x) # => (2+0i)
Complex.json_create(y) # => (2.0+4i)

conj → complex

Returns the conjugate of self, Complex.rect(self.imag, self.real):

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

Alias for: conjugate

conjugate

Source

VALUE
rb_complex_conjugate(VALUE self)
{
    get_dat1(self);
    return f_complex_new2(CLASS_OF(self), dat->real, f_negate(dat->imag));
}

Also aliased as: conj

denominator → integer

Source

static VALUE
nucomp_denominator(VALUE self)
{
    get_dat1(self);
    return rb_lcm(f_denominator(dat->real), f_denominator(dat->imag));
}

Returns the denominator of self, which is the least common multiple of self.real.denominator and self.imag.denominator:

Complex.rect(Rational(1, 2), Rational(2, 3)).denominator # => 6

Note that n.denominator of a non-rational numeric is 1.

Related: Complex#numerator.

fdiv(numeric) → new_complex

Source

static VALUE
nucomp_fdiv(VALUE self, VALUE other)
{
    return f_divide(self, other, f_fdiv, id_fdiv);
}

Returns Complex.rect(self.real/numeric, self.imag/numeric):

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

finite? → true or false

Source

static VALUE
rb_complex_finite_p(VALUE self)
{
    get_dat1(self);

    return RBOOL(f_finite_p(dat->real) && f_finite_p(dat->imag));
}

Returns true if both self.real.finite? and self.imag.finite? are true, false otherwise:

Complex.rect(1, 1).finite?               # => true
Complex.rect(Float::INFINITY, 0).finite? # => false

hash → integer

Source

static VALUE
nucomp_hash(VALUE self)
{
    return ST2FIX(rb_complex_hash(self));
}

Returns the integer hash value for self.

Two Complex objects created from the same values will have the same hash value (and will compare using eql?):

Complex.rect(1, 2).hash == Complex.rect(1, 2).hash # => true

imag → numeric

Returns the imaginary value for self:

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

If self was created with polar coordinates, the returned value is computed, and may be inexact:

Complex.polar(1, Math::PI/4).imag # => 0.7071067811865476 # Square root of 2.

Alias for: imaginary

imaginary

Source

VALUE
rb_complex_imag(VALUE self)
{
    get_dat1(self);
    return dat->imag;
}

Also aliased as: imag

infinite? → 1 or nil

Source

static VALUE
rb_complex_infinite_p(VALUE self)
{
    get_dat1(self);

    if (!f_infinite_p(dat->real) && !f_infinite_p(dat->imag)) {
        return Qnil;
    }
    return ONE;
}

Returns 1 if either self.real.infinite? or self.imag.infinite? is true, nil otherwise:

Complex.rect(Float::INFINITY, 0).infinite? # => 1
Complex.rect(1, 1).infinite?               # => nil

inspect → string

Source

static VALUE
nucomp_inspect(VALUE self)
{
    VALUE s;

    s = rb_usascii_str_new2("(");
    f_format(self, s, rb_inspect);
    rb_str_cat2(s, ")");

    return s;
}

Returns a string representation of self:

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

magnitude

Alias for: abs

numerator → new_complex

Source

static VALUE
nucomp_numerator(VALUE self)
{
    VALUE cd;

    get_dat1(self);

    cd = nucomp_denominator(self);
    return f_complex_new2(CLASS_OF(self),
                          f_mul(f_numerator(dat->real),
                                f_div(cd, f_denominator(dat->real))),
                          f_mul(f_numerator(dat->imag),
                                f_div(cd, f_denominator(dat->imag))));
}

Returns the Complex object created from the numerators of the real and imaginary parts of self, after converting each part to the lowest common denominator of the two:

c = Complex.rect(Rational(2, 3), Rational(3, 4)) # => ((2/3)+(3/4)*i)
c.numerator                                      # => (8+9i)

In this example, the lowest common denominator of the two parts is 12; the two converted parts may be thought of as Rational(8, 12) and Rational(9, 12), whose numerators, respectively, are 8 and 9; so the returned value of c.numerator is Complex.rect(8, 9).

Related: Complex#denominator.

phase

Alias for: arg

polar → array

Source

static VALUE
nucomp_polar(VALUE self)
{
    return rb_assoc_new(f_abs(self), f_arg(self));
}

Returns the array [self.abs, self.arg]:

Complex.polar(1, 2).polar # => [1.0, 2.0]

See Polar Coordinates.

If self was created with rectangular coordinates, the returned value is computed, and may be inexact:

Complex.rect(1, 1).polar # => [1.4142135623730951, 0.7853981633974483]

self / other → complex

Source

VALUE
rb_complex_div(VALUE self, VALUE other)
{
    return f_divide(self, other, f_quo, id_quo);
}

Returns the quotient of self and other:

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

rationalize(epsilon = nil) → rational

Source

static VALUE
nucomp_rationalize(int argc, VALUE *argv, VALUE self)
{
    get_dat1(self);

    rb_check_arity(argc, 0, 1);

    if (!k_exact_zero_p(dat->imag)) {
       rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Rational",
                self);
    }
    return rb_funcallv(dat->real, id_rationalize, argc, argv);
}

Returns a Rational object whose value is exactly or approximately equivalent to that of self.real.

With no argument epsilon given, returns a Rational object whose value is exactly equal to that of self.real.rationalize:

Complex.rect(1, 0).rationalize              # => (1/1)
Complex.rect(1, Rational(0, 1)).rationalize # => (1/1)
Complex.rect(3.14159, 0).rationalize        # => (314159/100000)

With argument epsilon given, returns a Rational object whose value is exactly or approximately equal to that of self.real to the given precision:

Complex.rect(3.14159, 0).rationalize(0.1)          # => (16/5)
Complex.rect(3.14159, 0).rationalize(0.01)         # => (22/7)
Complex.rect(3.14159, 0).rationalize(0.001)        # => (201/64)
Complex.rect(3.14159, 0).rationalize(0.0001)       # => (333/106)
Complex.rect(3.14159, 0).rationalize(0.00001)      # => (355/113)
Complex.rect(3.14159, 0).rationalize(0.000001)     # => (7433/2366)
Complex.rect(3.14159, 0).rationalize(0.0000001)    # => (9208/2931)
Complex.rect(3.14159, 0).rationalize(0.00000001)   # => (47460/15107)
Complex.rect(3.14159, 0).rationalize(0.000000001)  # => (76149/24239)
Complex.rect(3.14159, 0).rationalize(0.0000000001) # => (314159/100000)
Complex.rect(3.14159, 0).rationalize(0.0)          # => (3537115888337719/1125899906842624)

Related: Complex#to_r.

real → numeric

Source

VALUE
rb_complex_real(VALUE self)
{
    get_dat1(self);
    return dat->real;
}

Returns the real value for self:

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

If self was created with polar coordinates, the returned value is computed, and may be inexact:

Complex.polar(1, Math::PI/4).real # => 0.7071067811865476 # Square root of 2.

real? → false

Source

static VALUE
nucomp_real_p_m(VALUE self)
{
    return Qfalse;
}

Returns false; for compatibility with Numeric#real?.

rect → array

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.

Alias for: rectangular

rectangular

Source

static VALUE
nucomp_rect(VALUE self)
{
    get_dat1(self);
    return rb_assoc_new(dat->real, dat->imag);
}

Also aliased as: rect, rect

to_c → self

Source

static VALUE
nucomp_to_c(VALUE self)
{
    return self;
}

Returns self.

to_d → bigdecimal

to_d(precision) → bigdecimal

Source

# File bundled-src/bigdecimal-4.0.1/lib/bigdecimal/util.rb, line 164
def to_d(precision=0)
  BigDecimal(self) unless self.imag.zero? # to raise error

  BigDecimal(self.real, precision)
end

Returns the value as a BigDecimal. If the imaginary part is not 0, an error is raised

The precision parameter is used to determine the number of significant digits for the result. When precision is set to 0, the number of digits to represent the float being converted is determined automatically. The default precision is 0.

require 'bigdecimal'
require 'bigdecimal/util'

Complex(0.1234567, 0).to_d(4)   # => 0.1235e0
Complex(Rational(22, 7), 0).to_d(3)   # => 0.314e1
Complex(1, 1).to_d   # raises ArgumentError

class Complex

Performing Complex Arithmetic

Performing `Complex` Arithmetic