class Complex - RDoc Documentation

# class Complex

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:

- A complex literal.

You can convert certain objects to Complex objects with:

- Method Complex.

`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

I

  The imaginary unit.

### Public Class Methods

json_create(object) click to toggle source

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

    # File ext/json/lib/json/add/complex.rb, line 10
    def self.json_create(object)
      Complex(object['r'], object['i'])
    end

polar(abs[, arg]) → complex click to toggle source

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)

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

        argc = rb_scan_args(argc, argv, "11", &abs, &arg);
        nucomp_real_check(abs);
        if (argc == 2) {
            nucomp_real_check(arg);
        }
        else {
            arg = ZERO;
        }
        if (RB_TYPE_P(abs, T_COMPLEX)) {
            get_dat1(abs);
            abs = dat->real;
        }
        if (RB_TYPE_P(arg, T_COMPLEX)) {
            get_dat1(arg);
            arg = dat->real;
        }
        return f_complex_polar(klass, abs, arg);
    }

rect(real[, imag]) → complex click to toggle source
rectangular(real[, imag]) → complex

Returns a complex object which denotes the given rectangular form.

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

    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:
            nucomp_real_check(real);
            imag = ZERO;
            break;
          default:
            nucomp_real_check(real);
            nucomp_real_check(imag);
            break;
        }

        return nucomp_s_canonicalize_internal(klass, real, imag);
    }

rect(real[, imag]) → complex click to toggle source
rectangular(real[, imag]) → complex

Returns a complex object which denotes the given rectangular form.

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

    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:
            nucomp_real_check(real);
            imag = ZERO;
            break;
          default:
            nucomp_real_check(real);
            nucomp_real_check(imag);
            break;
        }

        return nucomp_s_canonicalize_internal(klass, real, imag);
    }

### Public Instance Methods

cmp * numeric → complex click to toggle source

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)

    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, '*');
    }

cmp ** numeric → complex click to toggle source

Performs exponentiation.

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

    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 (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);
    }

cmp + numeric → complex click to toggle source

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)

    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, '+');
    }

cmp - numeric → complex click to toggle source

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)

    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, '-');
    }

-cmp → complex click to toggle source

Returns negation of the value.

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

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

cmp / numeric → complex click to toggle source
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)

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

cmp <=> object → 0, 1, -1, or nil click to toggle source

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

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

cmp == object → true or false click to toggle source

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

    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));
    }

abs → real click to toggle source

Returns the absolute part of its polar form.

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

    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);
    }

Also aliased as: magnitude
abs2 → real click to toggle source

Returns square of the absolute value.

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

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

angle → float

Returns the angle part of its polar form.

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

Alias for: arg
arg → float click to toggle source

Returns the angle part of its polar form.

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

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

Also aliased as: angle, phase
as_json(*) click to toggle source

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

    # File ext/json/lib/json/add/complex.rb, line 16
    def as_json(*)
      {
        JSON.create_id => self.class.name,
        'r'            => real,
        'i'            => imag,
      }
    end

conj → complex

Returns the complex conjugate.

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

Alias for: conjugate
conjugate -> complex click to toggle source

Returns the complex conjugate.

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

    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 click to toggle source

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

See numerator.

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

fdiv(numeric) → complex click to toggle source

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

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

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

finite? → true or false click to toggle source

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

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

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

hash() click to toggle source

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

imag → real

Returns the imaginary part.

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

Alias for: imaginary
imaginary -> real click to toggle source

Returns the imaginary part.

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

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

Also aliased as: imag
infinite? → nil or 1 click to toggle source

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

    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;
    }

inspect → string click to toggle source

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)"

    static VALUE
    nucomp_inspect(VALUE self)
    {
        VALUE s;

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

        return s;
    }

magnitude → real

Returns the absolute part of its polar form.

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

Alias for: abs
numerator → numeric click to toggle source

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.

    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))));
    }

phase → float

Returns the angle part of its polar form.

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

Alias for: arg
polar → array click to toggle source

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

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

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

cmp / numeric → complex click to toggle source
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)

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

rationalize([eps]) → rational click to toggle source

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.

    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);
    }

real → real click to toggle source

Returns the real part.

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

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

Complex(1).real? → false click to toggle source
Complex(1, 2).real? → false

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

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

rect → array

Returns a complex object which denotes the given rectangular form.

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

Alias for: rectangular
rectangular -> array click to toggle source

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

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

    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 click to toggle source

Returns self.

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

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

to_d → bigdecimal click to toggle source
to_d(precision) → bigdecimal

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`.

    # File ext/bigdecimal/lib/bigdecimal/util.rb, line 153
    def to_d(*args)
      BigDecimal(self) unless self.imag.zero? # to raise eerror

      if args.length == 0
        case self.real
        when Rational
          BigDecimal(self.real) # to raise error
        end
      end
      self.real.to_d(*args)
    end

to_f → float click to toggle source

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

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

        if (!k_exact_zero_p(dat->imag)) {
            rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Float",
                     self);
        }
        return f_to_f(dat->real);
    }

to_i → integer click to toggle source

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

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

        if (!k_exact_zero_p(dat->imag)) {
            rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Integer",
                     self);
        }
        return f_to_i(dat->real);
    }

to_json(*args) click to toggle source

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

    # File ext/json/lib/json/add/complex.rb, line 25
    def to_json(*args)
      as_json.to_json(*args)
    end

to_r → rational click to toggle source

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.

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

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

to_s → string click to toggle source

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"

    static VALUE
    nucomp_to_s(VALUE self)
    {
        return f_format(self, rb_String);
    }