Class: Complex

Inherits:
Numeric show all
Defined in:
complex.c

Overview

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.

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)

Defined Under Namespace

Classes: compatible

Constant Summary collapse

I =

The imaginary unit.

f_complex_new_bang2(rb_cComplex, ZERO, ONE)

Class Method Summary collapse

Instance Method Summary collapse

Methods inherited from Numeric

#%, #+@, #<=>, #ceil, #div, #divmod, #floor, #i, #initialize_copy, #integer?, #modulo, #negative?, #nonzero?, #positive?, #remainder, #round, #singleton_method_added, #step, #to_int, #truncate, #zero?

Methods included from Comparable

#<, #<=, #>, #>=, #between?

Class Method Details

.polar(abs[, arg]) ⇒ 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)



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# File 'complex.c', line 618

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

    switch (rb_scan_args(argc, argv, "11", &abs, &arg)) {
      case 1:
	nucomp_real_check(abs);
	if (canonicalization) return abs;
	return nucomp_s_new_internal(klass, abs, ZERO);
      default:
	nucomp_real_check(abs);
	nucomp_real_check(arg);
	break;
    }
    return f_complex_polar(klass, abs, arg);
}

.rect(real[, imag]) ⇒ Object .rectangular(real[, imag]) ⇒ Object

Returns a complex object which denotes the given rectangular form.

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



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# File 'complex.c', line 412

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]) ⇒ Object .rectangular(real[, imag]) ⇒ Object

Returns a complex object which denotes the given rectangular form.

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



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# File 'complex.c', line 412

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);
}

Instance Method Details

#* ⇒ Object

#**(numeric) ⇒ Object

Performs exponentiation.

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



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# File 'complex.c', line 906

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

    if (k_rational_p(other) && f_one_p(f_denominator(other)))
	other = f_numerator(other); /* c14n */

    if (k_complex_p(other)) {
	get_dat1(other);

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

    if (k_complex_p(other)) {
	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 (k_fixnum_p(other)) {
	if (f_gt_p(other, ZERO)) {
	    VALUE x, z;
	    long n;

	    x = self;
	    z = x;
	    n = FIX2LONG(other) - 1;

	    while (n) {
		long q, r;

		while (1) {
		    get_dat1(x);

		    q = n / 2;
		    r = n % 2;

		    if (r)
			break;

		    x = nucomp_s_new_internal(CLASS_OF(self),
				       f_sub(f_mul(dat->real, dat->real),
					     f_mul(dat->imag, dat->imag)),
				       f_mul(f_mul(TWO, dat->real), dat->imag));
		    n = q;
		}
		z = f_mul(z, x);
		n--;
	    }
	    return z;
	}
	return f_expt(f_reciprocal(self), f_negate(other));
    }
    if (k_numeric_p(other) && f_real_p(other)) {
	VALUE r, theta;

	if (k_bignum_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);
}

#+ ⇒ Object

#-(numeric) ⇒ Object

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)



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# File 'complex.c', line 739

static VALUE
nucomp_sub(VALUE self, VALUE other)
{
    return f_addsub(self, other, f_sub, '-');
}

#- ⇒ Object

Returns negation of the value.

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



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# File 'complex.c', line 677

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

#/(numeric) ⇒ Object #quo(numeric) ⇒ Object

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)



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# File 'complex.c', line 869

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

#==(object) ⇒ Boolean

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:

  • (Boolean) 


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# File 'complex.c', line 997

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

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

#abs ⇒ Object #magnitude ⇒ Object

Returns the absolute part of its polar form.

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



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# File 'complex.c', line 1038

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

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

#abs2 ⇒ Object

Returns square of the absolute value.

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



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# File 'complex.c', line 1067

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

#arg ⇒ Float #angle ⇒ Float #phase ⇒ Float

Returns the angle part of its polar form.

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

Overloads:



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# File 'complex.c', line 1085

static VALUE
nucomp_arg(VALUE self)
{
    get_dat1(self);
    return m_atan2_bang(dat->imag, dat->real);
}

#arg ⇒ Float #angle ⇒ Float #phase ⇒ Float

Returns the angle part of its polar form.

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

Overloads:



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# File 'complex.c', line 1085

static VALUE
nucomp_arg(VALUE self)
{
    get_dat1(self);
    return m_atan2_bang(dat->imag, dat->real);
}

#coerce(other) ⇒ Object

:nodoc:



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# File 'complex.c', line 1015

static VALUE
nucomp_coerce(VALUE self, VALUE other)
{
    if (k_numeric_p(other) && f_real_p(other))
	return rb_assoc_new(f_complex_new_bang1(CLASS_OF(self), other), self);
    if (RB_TYPE_P(other, T_COMPLEX))
	return rb_assoc_new(other, self);

    rb_raise(rb_eTypeError, "%"PRIsVALUE" can't be coerced into %"PRIsVALUE,
	     rb_obj_class(other), rb_obj_class(self));
    return Qnil;
}

#complex? ⇒ Boolean

:nodoc:

Returns:

  • (Boolean) 


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# File 'complex.c', line 1140

static VALUE
nucomp_true(VALUE self)
{
    return Qtrue;
}

#conj ⇒ Object #conjugate ⇒ Object

Returns the complex conjugate.

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



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# File 'complex.c', line 1131

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

#conj ⇒ Object #conjugate ⇒ Object

Returns the complex conjugate.

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



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# File 'complex.c', line 1131

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

#denominator ⇒ Integer

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

See numerator.

Returns:



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# File 'complex.c', line 1184

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

#eql?(other) ⇒ Boolean

:nodoc:

Returns:

  • (Boolean) 


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# File 'complex.c', line 1241

static VALUE
nucomp_eql_p(VALUE self, VALUE other)
{
    if (k_complex_p(other)) {
	get_dat2(self, other);

	return f_boolcast((CLASS_OF(adat->real) == CLASS_OF(bdat->real)) &&
			  (CLASS_OF(adat->imag) == CLASS_OF(bdat->imag)) &&
			  f_eqeq_p(self, other));

    }
    return Qfalse;
}

#exact? ⇒ Boolean

:nodoc:

Returns:

  • (Boolean) 


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# File 'complex.c', line 1161

static VALUE
nucomp_exact_p(VALUE self)
{
    get_dat1(self);
    return f_boolcast(k_exact_p(dat->real) && k_exact_p(dat->imag));
}

#fdiv(numeric) ⇒ Object

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

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



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# File 'complex.c', line 885

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

#hash ⇒ Object

:nodoc:



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# File 'complex.c', line 1225

static VALUE
nucomp_hash(VALUE self)
{
    st_index_t v, h[2];
    VALUE n;

    get_dat1(self);
    n = rb_hash(dat->real);
    h[0] = NUM2LONG(n);
    n = rb_hash(dat->imag);
    h[1] = NUM2LONG(n);
    v = rb_memhash(h, sizeof(h));
    return LONG2FIX(v);
}

#imag ⇒ Object #imaginary ⇒ Object

Returns the imaginary part.

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



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# File 'complex.c', line 662

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

#imag ⇒ Object #imaginary ⇒ Object

Returns the imaginary part.

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



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# File 'complex.c', line 662

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

#inexact? ⇒ Boolean

:nodoc:

Returns:

  • (Boolean) 


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# File 'complex.c', line 1169

static VALUE
nucomp_inexact_p(VALUE self)
{
    return f_boolcast(!nucomp_exact_p(self));
}

#inspect ⇒ String

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:



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# File 'complex.c', line 1321

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;
}

#abs ⇒ Object #magnitude ⇒ Object

Returns the absolute part of its polar form.

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



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# File 'complex.c', line 1038

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

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

#marshal_dump ⇒ Object (private)

:nodoc:



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# File 'complex.c', line 1353

static VALUE
nucomp_marshal_dump(VALUE self)
{
    VALUE a;
    get_dat1(self);

    a = rb_assoc_new(dat->real, dat->imag);
    rb_copy_generic_ivar(a, self);
    return a;
}

#numerator ⇒ Numeric

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:



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# File 'complex.c', line 1209

static VALUE
nucomp_numerator(VALUE self)
{
    VALUE cd;

    get_dat1(self);

    cd = f_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))));
}

#arg ⇒ Float #angle ⇒ Float #phase ⇒ Float

Returns the angle part of its polar form.

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

Overloads:



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# File 'complex.c', line 1085

static VALUE
nucomp_arg(VALUE self)
{
    get_dat1(self);
    return m_atan2_bang(dat->imag, dat->real);
}

#polar ⇒ Array

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

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

Returns:



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# File 'complex.c', line 1116

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

#quo ⇒ Object

#rationalize([eps]) ⇒ Object

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.



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# File 'complex.c', line 1505

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

    rb_scan_args(argc, argv, "01", NULL);

    if (!k_exact_zero_p(dat->imag)) {
       rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Rational",
                self);
    }
    return rb_funcall2(dat->real, rb_intern("rationalize"), argc, argv);
}

#real ⇒ Object

Returns the real part.

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



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# File 'complex.c', line 645

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

#real? ⇒ false

Returns false.

Returns:

  • (false)

Returns:

  • (Boolean) 


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# File 'complex.c', line 1153

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

#rect ⇒ Array #rectangular ⇒ Array

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

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

Overloads:



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# File 'complex.c', line 1101

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

#rect ⇒ Array #rectangular ⇒ Array

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

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

Overloads:



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# File 'complex.c', line 1101

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

#to_c ⇒ self

Returns self.

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

Returns:

  • (self) 


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# File 'complex.c', line 1528

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

#to_f ⇒ Float

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:



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# File 'complex.c', line 1455

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

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

Returns:



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# File 'complex.c', line 1432

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_r ⇒ Object

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.



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# File 'complex.c', line 1480

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

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"

Returns:



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# File 'complex.c', line 1303

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

#conj ⇒ Object #conjugate ⇒ Object

Returns the complex conjugate.

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



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# File 'complex.c', line 1131

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