# 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.

In ruby, you can create complex object with Complex, Complex::rect, Complex::polar or to_c method.

``````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('[email protected]')       #=> (-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)
'[email protected]'.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

• Returns a complex object which denotes the given polar form.

• Returns a complex object which denotes the given rectangular form.

• Returns a complex object which denotes the given rectangular form.

## Instance Method Summary collapse

• Performs multiplication.

• Performs exponentiation.

• Performs subtraction.

• Returns negation of the value.

• Performs division.

• Returns true if cmp equals object numerically.

• Returns the absolute part of its polar form.

• Returns square of the absolute value.

• Returns the angle part of its polar form.

• Returns the angle part of its polar form.

• :nodoc:.

• :nodoc:.

• Returns the complex conjugate.

• Returns the complex conjugate.

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

• :nodoc:.

• :nodoc:.

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

• :nodoc:.

• Returns the imaginary part.

• Returns the imaginary part.

• :nodoc:.

• Returns the value as a string for inspection.

• Returns the absolute part of its polar form.

• private

:nodoc:.

• Returns the numerator.

• Returns the angle part of its polar form.

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

• Returns the value as a rational if possible (the imaginary part should be exactly zero).

• Returns the real part.

• Returns false.

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

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

• Returns self.

• Returns the value as a float if possible (the imaginary part should be exactly zero).

• Returns the value as an integer if possible (the imaginary part should be exactly zero).

• Returns the value as a rational if possible (the imaginary part should be exactly zero).

• Returns the value as a string.

• Returns the complex conjugate.

## 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)
``````
 ``` 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616``` ```# File 'complex.c', line 600 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); arg = ZERO; break; 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)
``````
 ``` 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462``` ```# File 'complex.c', line 445 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)
``````
 ``` 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462``` ```# File 'complex.c', line 445 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

### #*(numeric) ⇒ Object

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)
``````
 ``` 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761``` ```# File 'complex.c', line 738 static VALUE nucomp_mul(VALUE self, VALUE other) { if (k_complex_p(other)) { VALUE real, imag; get_dat2(self, other); real = f_sub(f_mul(adat->real, bdat->real), f_mul(adat->imag, bdat->imag)); imag = f_add(f_mul(adat->real, bdat->imag), f_mul(adat->imag, bdat->real)); 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, '*'); }```

### #**(numeric) ⇒ Object

Performs exponentiation.

``````Complex('i') ** 2              #=> (-1+0i)
Complex(-8) ** Rational(1, 3)  #=> (1.0000000000000002+1.7320508075688772i)
``````
 ``` 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944``` ```# File 'complex.c', line 867 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); }```

### #+(numeric) ⇒ Object

``````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)
``````
 ``` 702 703 704 705 706``` ```# File 'complex.c', line 702 static VALUE nucomp_add(VALUE self, VALUE other) { return f_addsub(self, other, f_add, '+'); }```

### #-(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)
``````
 ``` 720 721 722 723 724``` ```# File 'complex.c', line 720 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)
``````
 ``` 659 660 661 662 663 664 665``` ```# File 'complex.c', line 659 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)
``````
 ``` 830 831 832 833 834``` ```# File 'complex.c', line 830 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)
 ``` 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973``` ```# File 'complex.c', line 958 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
``````
 ``` 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017``` ```# File 'complex.c', line 999 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
``````
 ``` 1028 1029 1030 1031 1032 1033 1034``` ```# File 'complex.c', line 1028 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
``````

 ``` 1046 1047 1048 1049 1050 1051``` ```# File 'complex.c', line 1046 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
``````

 ``` 1046 1047 1048 1049 1050 1051``` ```# File 'complex.c', line 1046 static VALUE nucomp_arg(VALUE self) { get_dat1(self); return m_atan2_bang(dat->imag, dat->real); }```

### #coerce ⇒ Object

:nodoc:

 ``` 976 977 978 979 980 981 982 983 984 985 986 987``` ```# File 'complex.c', line 976 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, "%s can't be coerced into %s", rb_obj_classname(other), rb_obj_classname(self)); return Qnil; }```

### #complex? ⇒ Boolean

:nodoc:

Returns:

• (Boolean)
 ``` 1101 1102 1103 1104 1105``` ```# File 'complex.c', line 1101 static VALUE nucomp_true(VALUE self) { return Qtrue; }```

### #conj ⇒ Object #conjugate ⇒ Object

Returns the complex conjugate.

``````Complex(1, 2).conjugate  #=> (1-2i)
``````
 ``` 1092 1093 1094 1095 1096 1097``` ```# File 'complex.c', line 1092 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)
``````
 ``` 1092 1093 1094 1095 1096 1097``` ```# File 'complex.c', line 1092 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:

 ``` 1145 1146 1147 1148 1149 1150``` ```# File 'complex.c', line 1145 static VALUE nucomp_denominator(VALUE self) { get_dat1(self); return rb_lcm(f_denominator(dat->real), f_denominator(dat->imag)); }```

### #eql? ⇒ Boolean

:nodoc:

Returns:

• (Boolean)
 ``` 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214``` ```# File 'complex.c', line 1202 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)
 ``` 1122 1123 1124 1125 1126 1127``` ```# File 'complex.c', line 1122 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)
``````
 ``` 846 847 848 849 850``` ```# File 'complex.c', line 846 static VALUE nucomp_fdiv(VALUE self, VALUE other) { return f_divide(self, other, f_fdiv, id_fdiv); }```

### #hash ⇒ Object

:nodoc:

 ``` 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199``` ```# File 'complex.c', line 1186 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
``````
 ``` 644 645 646 647 648 649``` ```# File 'complex.c', line 644 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
``````
 ``` 644 645 646 647 648 649``` ```# File 'complex.c', line 644 static VALUE nucomp_imag(VALUE self) { get_dat1(self); return dat->imag; }```

### #inexact? ⇒ Boolean

:nodoc:

Returns:

• (Boolean)
 ``` 1130 1131 1132 1133 1134``` ```# File 'complex.c', line 1130 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:

 ``` 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298``` ```# File 'complex.c', line 1288 static VALUE nucomp_inspect(VALUE self) { VALUE s; s = rb_usascii_str_new2("("); rb_str_concat(s, f_format(self, f_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
``````
 ``` 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017``` ```# File 'complex.c', line 999 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:

 ``` 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329``` ```# File 'complex.c', line 1320 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:

 ``` 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183``` ```# File 'complex.c', line 1170 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
``````

 ``` 1046 1047 1048 1049 1050 1051``` ```# File 'complex.c', line 1046 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:

 ``` 1077 1078 1079 1080 1081``` ```# File 'complex.c', line 1077 static VALUE nucomp_polar(VALUE self) { return rb_assoc_new(f_abs(self), f_arg(self)); }```

### #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.

 ``` 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474``` ```# File 'complex.c', line 1461 static VALUE nucomp_rationalize(int argc, VALUE *argv, VALUE self) { get_dat1(self); rb_scan_args(argc, argv, "01", NULL); if (k_inexact_p(dat->imag) || f_nonzero_p(dat->imag)) { VALUE s = f_to_s(self); rb_raise(rb_eRangeError, "can't convert %s into Rational", StringValuePtr(s)); } 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
``````
 ``` 627 628 629 630 631 632``` ```# File 'complex.c', line 627 static VALUE nucomp_real(VALUE self) { get_dat1(self); return dat->real; }```

### #real? ⇒ false

Returns false.

Returns:

• (false)

Returns:

• (Boolean)
 ``` 1114 1115 1116 1117 1118``` ```# File 'complex.c', line 1114 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]
``````

 ``` 1062 1063 1064 1065 1066 1067``` ```# File 'complex.c', line 1062 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]
``````

 ``` 1062 1063 1064 1065 1066 1067``` ```# File 'complex.c', line 1062 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)
 ``` 1485 1486 1487 1488 1489``` ```# File 'complex.c', line 1485 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:

 ``` 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420``` ```# File 'complex.c', line 1409 static VALUE nucomp_to_f(VALUE self) { get_dat1(self); if (k_inexact_p(dat->imag) || f_nonzero_p(dat->imag)) { VALUE s = f_to_s(self); rb_raise(rb_eRangeError, "can't convert %s into Float", StringValuePtr(s)); } 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:

 ``` 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396``` ```# File 'complex.c', line 1385 static VALUE nucomp_to_i(VALUE self) { get_dat1(self); if (k_inexact_p(dat->imag) || f_nonzero_p(dat->imag)) { VALUE s = f_to_s(self); rb_raise(rb_eRangeError, "can't convert %s into Integer", StringValuePtr(s)); } 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.

 ``` 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446``` ```# File 'complex.c', line 1435 static VALUE nucomp_to_r(VALUE self) { get_dat1(self); if (k_inexact_p(dat->imag) || f_nonzero_p(dat->imag)) { VALUE s = f_to_s(self); rb_raise(rb_eRangeError, "can't convert %s into Rational", StringValuePtr(s)); } 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:

 ``` 1270 1271 1272 1273 1274``` ```# File 'complex.c', line 1270 static VALUE nucomp_to_s(VALUE self) { return f_format(self, f_to_s); }```

### #conj ⇒ Object #conjugate ⇒ Object

Returns the complex conjugate.

``````Complex(1, 2).conjugate  #=> (1-2i)
``````
 ``` 1092 1093 1094 1095 1096 1097``` ```# File 'complex.c', line 1092 static VALUE nucomp_conj(VALUE self) { get_dat1(self); return f_complex_new2(CLASS_OF(self), dat->real, f_negate(dat->imag)); }```