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Showing content from https://docs.ruby-lang.org/en/3.4/Complex.html below:

class Complex - Documentation for Ruby 3.4

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

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.

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:

• ::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.

• 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].

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

• ==: Returns whether self is equal to the given argument.

• 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.

• *: 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).

• ::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'

I

Equivalent to Complex.rect(0, 1):

Complex::I 

def self.json_create(object)
  Complex(object['r'], object['i'])
end

See as_json.

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)        
Complex.polar(3, 2.0)   
Complex.polar(-3, -2.0) 

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);
}

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; see Rectangular Coordinates:

Complex.rect(3)             
Complex.rect(3, Math::PI)   
Complex.rect(-3, -Math::PI) 

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);
}

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; see Rectangular Coordinates:

Complex.rect(3)             
Complex.rect(3, Math::PI)   
Complex.rect(-3, -Math::PI) 

Complex.rectangular is an alias for Complex.rect.

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 product of self and numeric:

Complex.rect(2, 3)  * Complex.rect(2, 3)  
Complex.rect(900)   * Complex.rect(1)     
Complex.rect(-2, 9) * Complex.rect(-9, 2) 
Complex.rect(9, 8)  * 4                   
Complex.rect(20, 9) * 9.8                 

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 power numeric:

Complex.rect(0, 1) ** 2            
Complex.rect(-8) ** Rational(1, 3) 

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 numeric:

Complex.rect(2, 3)  + Complex.rect(2, 3)  
Complex.rect(900)   + Complex.rect(1)     
Complex.rect(-2, 9) + Complex.rect(-9, 2) 
Complex.rect(9, 8)  + 4                   
Complex.rect(20, 9) + 9.8                 

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 numeric:

Complex.rect(2, 3)  - Complex.rect(2, 3)  
Complex.rect(900)   - Complex.rect(1)     
Complex.rect(-2, 9) - Complex.rect(-9, 2) 
Complex.rect(9, 8)  - 4                   
Complex.rect(20, 9) - 9.8                 

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

-Complex.rect(1, 2)   
-Complex.rect(-1, -2) 

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

Returns the quotient of self and numeric:

Complex.rect(2, 3)  / Complex.rect(2, 3)  
Complex.rect(900)   / Complex.rect(1)     
Complex.rect(-2, 9) / Complex.rect(-9, 2) 
Complex.rect(9, 8)  / 4                   
Complex.rect(20, 9) / 9.8                 

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;
}

Returns:

• self.real <=> object.real if both of the following are true:

  • self.imag == 0.

  • object.imag == 0. # Always true if object is numeric but not complex.

• nil otherwise.

Examples:

Complex.rect(2) <=> 3                  
Complex.rect(2) <=> 2                  
Complex.rect(2) <=> 1                  
Complex.rect(2, 1) <=> 1               
Complex.rect(1) <=> Complex.rect(1, 1) 
Complex.rect(1) <=> 'Foo'              

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) 

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 

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

Complex.rectangular(1, 1).abs 

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 

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 

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  

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

Complex.polar(1, 1.0/3).arg 

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      
y = Complex(2.0, 4).as_json 

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

Complex.json_create(x) 
Complex.json_create(y) 

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 

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

Related: Complex#numerator.

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?               
Complex.rect(Float::INFINITY, 0).finite? 

Related: Numeric#finite?, Float#finite?.

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 

Returns the imaginary value for self:

Complex.rect(7).imag     
Complex.rect(9, -4).imag 

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

Complex.polar(1, Math::PI/4).imag 

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? 
Complex.rect(1, 1).infinite?               

Related: Numeric#infinite?, Float#infinite?.

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                      
Complex.rect(-8, 6).inspect                  
Complex.rect(0, Rational(1, 2)).inspect      
Complex.rect(0, Float::INFINITY).inspect     
Complex.rect(Float::NAN, Float::NAN).inspect 

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)) 
c.numerator                                      

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.

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 

See Polar Coordinates.

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

Complex.rect(1, 1).polar 

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

Returns the quotient of self and numeric:

Complex.rect(2, 3)  / Complex.rect(2, 3)  
Complex.rect(900)   / Complex.rect(1)     
Complex.rect(-2, 9) / Complex.rect(-9, 2) 
Complex.rect(9, 8)  / 4                   
Complex.rect(20, 9) / 9.8                 

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              
Complex.rect(1, Rational(0, 1)).rationalize 
Complex.rect(3.14159, 0).rationalize        

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)          
Complex.rect(3.14159, 0).rationalize(0.01)         
Complex.rect(3.14159, 0).rationalize(0.001)        
Complex.rect(3.14159, 0).rationalize(0.0001)       
Complex.rect(3.14159, 0).rationalize(0.00001)      
Complex.rect(3.14159, 0).rationalize(0.000001)     
Complex.rect(3.14159, 0).rationalize(0.0000001)    
Complex.rect(3.14159, 0).rationalize(0.00000001)   
Complex.rect(3.14159, 0).rationalize(0.000000001)  
Complex.rect(3.14159, 0).rationalize(0.0000000001) 
Complex.rect(3.14159, 0).rationalize(0.0)          

Related: Complex#to_r.

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

Returns the real value for self:

Complex.rect(7).real     
Complex.rect(9, -4).real 

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

Complex.polar(1, Math::PI/4).real 

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

Returns false; for compatibility with Numeric#real?.

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; see Rectangular Coordinates:

Complex.rect(3)             
Complex.rect(3, Math::PI)   
Complex.rect(-3, -Math::PI) 

Complex.rectangular is an alias for Complex.rect.

Also aliased as:

, rect

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

Returns self.

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);
}

Returns the value of self.real as a Float, if possible:

Complex.rect(1, 0).to_f              
Complex.rect(1, Rational(0, 1)).to_f 

Raises RangeError if self.imag is not exactly zero (either Integer(0) or Rational(0, n)).

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);
}

Returns the value of self.real as an Integer, if possible:

Complex.rect(1, 0).to_i              
Complex.rect(1, Rational(0, 1)).to_i 

Raises RangeError if self.imag is not exactly zero (either Integer(0) or Rational(0, n)).

def to_json(*args)
  as_json.to_json(*args)
end

Returns a JSON string representing self:

require 'json/add/complex'
puts Complex(2).to_json
puts Complex(2.0, 4).to_json

Output:

{"json_class":"Complex","r":2,"i":0}
{"json_class":"Complex","r":2.0,"i":4}

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

    if (RB_FLOAT_TYPE_P(dat->imag) && FLOAT_ZERO_P(dat->imag)) {
        /* Do nothing here */
    }
    else if (!k_exact_zero_p(dat->imag)) {
        VALUE imag = rb_check_convert_type_with_id(dat->imag, T_RATIONAL, "Rational", idTo_r);
        if (NIL_P(imag) || !k_exact_zero_p(imag)) {
            rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Rational",
                     self);
        }
    }
    return f_to_r(dat->real);
}

Returns the value of self.real as a Rational, if possible:

Complex.rect(1, 0).to_r              
Complex.rect(1, Rational(0, 1)).to_r 
Complex.rect(1, 0.0).to_r            

Raises RangeError if self.imag is not exactly zero (either Integer(0) or Rational(0, n)) and self.imag.to_r is not exactly zero.

Related: Complex#rationalize.

static VALUE
nucomp_to_s(VALUE self)
{
    return f_format(self, rb_usascii_str_new2(""), rb_String);
}

Returns a string representation of self:

Complex.rect(2).to_s                      
Complex.rect(-8, 6).to_s                  
Complex.rect(0, Rational(1, 2)).to_s      
Complex.rect(0, Float::INFINITY).to_s     
Complex.rect(Float::NAN, Float::NAN).to_s 

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