ÿØÿà JFIF    ÿÛ „ ( %!1!%*+...983,7(-.- PKB]+ \\ to_r-i.rinu[U:RDoc::AnyMethod[iI" to_r:ETI"Complex#to_r;TF: privateo:RDoc::Markup::Document: @parts[ o:RDoc::Markup::Paragraph; [I"EReturns the value as a rational if possible (the imaginary part ;TI"should be exactly zero).;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [I"%Complex(1, 0).to_r #=> (1/1) ;TI"(Complex(1, 0.0).to_r # RangeError ;TI"(Complex(1, 2).to_r # RangeError ;T: @format0o; ; [I"See rationalize.;T: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0I"cmp.to_r -> rational ;T0[I"();T@FI" Complex;TcRDoc::NormalClass00PKB],ľ phase-i.rinu[U:RDoc::AnyMethod[iI" phase:ETI"Complex#phase;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I".Returns the angle part of its polar form.;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [I"=Complex.polar(3, Math::PI/2).arg #=> 1.5707963267948966;T: @format0: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below000[I"();T@FI" Complex;TcRDoc::NormalClass0[@FI"arg;TPKB]D inspect-i.rinu[U:RDoc::AnyMethod[iI" inspect:ETI"Complex#inspect;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I"2Returns the value as a string for inspection.;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [ I";Complex(2).inspect #=> "(2+0i)" ;TI"@Complex('-8/6').inspect #=> "((-4/3)+0i)" ;TI"@Complex('1/2i').inspect #=> "(0+(1/2)*i)" ;TI"CComplex(0, Float::INFINITY).inspect #=> "(0+Infinity*i)" ;TI"?Complex(Float::NAN, Float::NAN).inspect #=> "(NaN+NaN*i)";T: @format0: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0I"cmp.inspect -> string ;T0[I"();T@FI" Complex;TcRDoc::NormalClass00PKB]2 fdiv-i.rinu[U:RDoc::AnyMethod[iI" fdiv:ETI"Complex#fdiv;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I"FPerforms division as each part is a float, never returns a float.;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [I"IComplex(11, 22).fdiv(3) #=> (3.6666666666666665+7.333333333333333i);T: @format0: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0I"$cmp.fdiv(numeric) -> complex ;T0[I" (p1);T@FI" Complex;TcRDoc::NormalClass00PKB](r, imaginary ;TI"+value i, to a Complex object.;T: @fileI"%ext/json/lib/json/add/complex.rb;T:0@omit_headings_from_table_of_contents_below000[I" (object);T@FI" Complex;TcRDoc::NormalClass00PKB]BY polar-c.rinu[U:RDoc::AnyMethod[iI" polar:ETI"Complex::polar;TT: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I"AReturns a complex object which denotes the given polar form.;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [ I"3Complex.polar(3, 0) #=> (3.0+0.0i) ;TI"EComplex.polar(3, Math::PI/2) #=> (1.836909530733566e-16+3.0i) ;TI"FComplex.polar(3, Math::PI) #=> (-3.0+3.673819061467132e-16i) ;TI"DComplex.polar(3, -Math::PI/2) #=> (1.836909530733566e-16-3.0i);T: @format0: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0I",Complex.polar(abs[, arg]) -> complex ;T0[I"(p1, p2 = v2);T@FI" Complex;TcRDoc::NormalClass00PKB] rect-i.rinu[U:RDoc::AnyMethod[iI" rect:ETI"Complex#rect;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I"GReturns a complex object which denotes the given rectangular form.;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [I"*Complex.rectangular(1, 2) #=> (1+2i);T: @format0: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below000[I"();T@FI" Complex;TcRDoc::NormalClass0[@FI"rectangular;TPKB]g imag-i.rinu[U:RDoc::AnyMethod[iI" imag:ETI"Complex#imag;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I" Returns the imaginary part.;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [I"%Complex(7).imaginary #=> 0 ;TI"%Complex(9, -4).imaginary #=> -4;T: @format0: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below000[I"();T@FI" Complex;TcRDoc::NormalClass0[@FI"imaginary;TPKB]1arg-i.rinu[U:RDoc::AnyMethod[iI"arg:ETI"Complex#arg;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I".Returns the angle part of its polar form.;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [I"=Complex.polar(3, Math::PI/2).arg #=> 1.5707963267948966;T: @format0: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0I"Dcmp.arg -> float cmp.angle -> float cmp.phase -> float ;T0[[I" angle;T@ [I" phase;T@ I"();T@FI" Complex;TcRDoc::NormalClass00PKB]rationalize-i.rinu[U:RDoc::AnyMethod[iI"rationalize:ETI"Complex#rationalize;TF: privateo:RDoc::Markup::Document: @parts[ o:RDoc::Markup::Paragraph; [I"EReturns the value as a rational if possible (the imaginary part ;TI"should be exactly zero).;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [I".Complex(1.0/3, 0).rationalize #=> (1/3) ;TI"1Complex(1, 0.0).rationalize # RangeError ;TI"1Complex(1, 2).rationalize # RangeError ;T: @format0o; ; [I"See to_r.;T: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0I"*cmp.rationalize([eps]) -> rational ;T0[I" (*args);T@FI" Complex;TcRDoc::NormalClass00PKB]}K angle-i.rinu[U:RDoc::AnyMethod[iI" angle:ETI"Complex#angle;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I".Returns the angle part of its polar form.;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [I"=Complex.polar(3, Math::PI/2).arg #=> 1.5707963267948966;T: @format0: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below000[I"();T@FI" Complex;TcRDoc::NormalClass0[@FI"arg;TPKB]" polar-i.rinu[U:RDoc::AnyMethod[iI" polar:ETI"Complex#polar;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I"*Returns an array; [cmp.abs, cmp.arg].;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [I"DComplex(1, 2).polar #=> [2.23606797749979, 1.1071487177940904];T: @format0: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0I"cmp.polar -> array ;T0[I"();T@FI" Complex;TcRDoc::NormalClass00PKB] Qfinite%3f-i.rinu[U:RDoc::AnyMethod[iI" finite?:ETI"Complex#finite?;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I"QReturns +true+ if +cmp+'s real and imaginary parts are both finite numbers, ;TI"otherwise returns +false+.;T: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0I"$cmp.finite? -> true or false ;T0[I"();T@FI" Complex;TcRDoc::NormalClass00PKB]Bmagnitude-i.rinu[U:RDoc::AnyMethod[iI"magnitude:ETI"Complex#magnitude;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I"1Returns the absolute part of its polar form.;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [I"#Complex(-1).abs #=> 1 ;TI"$Complex(3.0, -4.0).abs #=> 5.0;T: @format0: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below000[I"();T@FI" Complex;TcRDoc::NormalClass0[@FI"abs;TPKB]묮p77 to_i-i.rinu[U:RDoc::AnyMethod[iI" to_i:ETI"Complex#to_i;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I"EReturns the value as an integer if possible (the imaginary part ;TI"should be exactly zero).;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [I"!Complex(1, 0).to_i #=> 1 ;TI"(Complex(1, 0.0).to_i # RangeError ;TI"'Complex(1, 2).to_i # RangeError;T: @format0: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0I"cmp.to_i -> integer ;T0[I"();T@FI" Complex;TcRDoc::NormalClass00PKB]-%2a-i.rinu[U:RDoc::AnyMethod[iI"*:ETI"Complex#*;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I"Performs multiplication.;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [ I"3Complex(2, 3) * Complex(2, 3) #=> (-5+12i) ;TI"3Complex(900) * Complex(1) #=> (900+0i) ;TI"2Complex(-2, 9) * Complex(-9, 2) #=> (0-85i) ;TI"3Complex(9, 8) * 4 #=> (36+32i) ;TI"7Complex(20, 9) * 9.8 #=> (196.0+88.2i);T: @format0: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0I" cmp * numeric -> complex ;T0[I" (p1);T@FI" Complex;TcRDoc::NormalClass00PKB]Q conj-i.rinu[U:RDoc::AnyMethod[iI" conj:ETI"Complex#conj;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I"#Returns the complex conjugate.;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [I"(Complex(1, 2).conjugate #=> (1-2i);T: @format0: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below000[I"();T@FI" Complex;TcRDoc::NormalClass0[@FI"conjugate;TPKB]ᏓPii to_d-i.rinu[U:RDoc::AnyMethod[iI" to_d:ETI"Complex#to_d;TF: privateo:RDoc::Markup::Document: @parts[ o:RDoc::Markup::Paragraph; [I"'Returns the value as a BigDecimal.;To:RDoc::Markup::BlankLineo; ; [I"JThe +precision+ parameter is required for a rational complex number. ;TI"JThis parameter is used to determine the number of significant digits ;TI"for the result.;T@o:RDoc::Markup::Verbatim; [ I"require 'bigdecimal' ;TI"require 'bigdecimal/util' ;TI" ;TI"3Complex(0.1234567, 0).to_d(4) # => 0.1235e0 ;TI"8Complex(Rational(22, 7), 0).to_d(3) # => 0.314e1 ;T: @format0o; ; [I"See also BigDecimal::new.;T: @fileI"*ext/bigdecimal/lib/bigdecimal/util.rb;T:0@omit_headings_from_table_of_contents_below0I"Kcmp.to_d -> bigdecimal cmp.to_d(precision) -> bigdecimal ;T0[I" (*args);T@FI" Complex;TcRDoc::NormalClass00PKB] cdesc-Complex.rinu[U:RDoc::NormalClass[iI" Complex:ET@I" Numeric;To:RDoc::Markup::Document: @parts[o;;[o:RDoc::Markup::Paragraph;[ I"FA complex number can be represented as a paired real number with ;TI"Fimaginary unit; a+bi. Where a is real part, b is imaginary part ;TI":and i is imaginary unit. Real a equals complex a+0i ;TI"mathematically.;To:RDoc::Markup::BlankLineo; ;[I"6You can create a \Complex object explicitly with:;T@o:RDoc::Markup::List: @type: BULLET: @items[o:RDoc::Markup::ListItem: @label0;[o; ;[I"OA {complex literal}[doc/syntax/literals_rdoc.html#label-Complex+Literals].;T@o; ;[I">You can convert certain objects to \Complex objects with:;T@o; ; ; ;[o;;0;[o; ;[I"5\Method {Complex}[Kernel.html#method-i-Complex].;T@o; ;[I"AComplex object can be created as literal, and also by using ;TI"BKernel#Complex, Complex::rect, Complex::polar or to_c method.;T@o:RDoc::Markup::Verbatim;[ I"%2+1i #=> (2+1i) ;TI"%Complex(1) #=> (1+0i) ;TI"%Complex(2, 3) #=> (2+3i) ;TI"HComplex.polar(2, 3) #=> (-1.9799849932008908+0.2822400161197344i) ;TI"%3.to_c #=> (3+0i) ;T: @format0o; ;[I"GYou can also create complex object from floating-point numbers or ;TI" strings.;T@o;;[I"'Complex(0.3) #=> (0.3+0i) ;TI")Complex('0.3-0.5i') #=> (0.3-0.5i) ;TI".Complex('2/3+3/4i') #=> ((2/3)+(3/4)*i) ;TI"HComplex('1@2') #=> (-0.4161468365471424+0.9092974268256817i) ;TI" ;TI"'0.3.to_c #=> (0.3+0i) ;TI")'0.3-0.5i'.to_c #=> (0.3-0.5i) ;TI".'2/3+3/4i'.to_c #=> ((2/3)+(3/4)*i) ;TI"H'1@2'.to_c #=> (-0.4161468365471424+0.9092974268256817i) ;T;0o; ;[I">A complex object is either an exact or an inexact number.;T@o;;[I".Complex(1, 1) / 2 #=> ((1/2)+(1/2)*i) ;TI"(Complex(1, 1) / 2.0 #=> (0.5+0.5i);T;0: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0o;;[;I"*ext/bigdecimal/lib/bigdecimal/util.rb;T;0o;;[;I"%ext/json/lib/json/add/complex.rb;T;0;0;0[[U:RDoc::Constant[iI"I;TI"Complex::I;T: public0o;;[o; ;[I"The imaginary unit.;T;@I;0@I@cRDoc::NormalClass0[[[I" class;T[[;[[:protected[[: private[ [I"json_create;TI"%ext/json/lib/json/add/complex.rb;T[I" polar;TI"complex.c;T[I" rect;T@l[I"rectangular;T@l[I" instance;T[[;[[;[[;[-[I"*;T@l[I"**;T@l[I"+;T@l[I"-;T@l[I"-@;T@l[I"/;T@l[I"<=>;T@l[I"==;T@l[I"abs;T@l[I" abs2;T@l[I" angle;T@l[I"arg;T@l[I" as_json;T@i[I" conj;T@l[I"conjugate;T@l[I"denominator;T@l[I" fdiv;T@l[I" finite?;T@l[I" hash;T@l[I" imag;T@l[I"imaginary;T@l[I"infinite?;T@l[I" inspect;T@l[I"magnitude;T@l[I"numerator;T@l[I" phase;T@l[I" polar;T@l[I"quo;T@l[I"rationalize;T@l[I" real;T@l[I" real?;T@l[@n@l[I"rectangular;T@l[I" to_c;T@l[I" to_d;TI"*ext/bigdecimal/lib/bigdecimal/util.rb;T[I" to_f;T@l[I" to_i;T@l[I" to_json;T@i[I" to_r;T@l[I" to_s;T@l[[U:RDoc::Context::Section[i0o;;[;0;0[I"complex.c;TI"*ext/bigdecimal/lib/bigdecimal/util.rb;TI"%ext/json/lib/json/add/complex.rb;T@OcRDoc::TopLevelPKB]_ to_c-i.rinu[U:RDoc::AnyMethod[iI" to_c:ETI"Complex#to_c;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I"Returns self.;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [I"%Complex(2).to_c #=> (2+0i) ;TI"%Complex(-8, 6).to_c #=> (-8+6i);T: @format0: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0I"complex.to_c -> self ;T0[I"();T@FI" Complex;TcRDoc::NormalClass00PKB]YYinfinite%3f-i.rinu[U:RDoc::AnyMethod[iI"infinite?:ETI"Complex#infinite?;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I"JReturns +1+ if +cmp+'s real or imaginary part is an infinite number, ;TI"otherwise returns +nil+.;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [ I"For example: ;TI" ;TI"3 (1+1i).infinite? #=> nil ;TI"0 (Float::INFINITY + 1i).infinite? #=> 1;T: @format0: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0I"!cmp.infinite? -> nil or 1 ;T0[I"();T@FI" Complex;TcRDoc::NormalClass00PKB]GJD6conjugate-i.rinu[U:RDoc::AnyMethod[iI"conjugate:ETI"Complex#conjugate;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I"#Returns the complex conjugate.;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [I"(Complex(1, 2).conjugate #=> (1-2i);T: @format0: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0I";cmp.conj -> complex cmp.conjugate -> complex ;T0[[I" conj;T@ I"();T@FI" Complex;TcRDoc::NormalClass00PKB]'\ %2a%2a-i.rinu[U:RDoc::AnyMethod[iI"**:ETI"Complex#**;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I"Performs exponentiation.;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [I"0Complex('i') ** 2 #=> (-1+0i) ;TI"PComplex(-8) ** Rational(1, 3) #=> (1.0000000000000002+1.7320508075688772i);T: @format0: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0I"!cmp ** numeric -> complex ;T0[I" (p1);T@FI" Complex;TcRDoc::NormalClass00PKB]eimaginary-i.rinu[U:RDoc::AnyMethod[iI"imaginary:ETI"Complex#imaginary;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I" Returns the imaginary part.;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [I"%Complex(7).imaginary #=> 0 ;TI"%Complex(9, -4).imaginary #=> -4;T: @format0: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0I"5cmp.imag -> real cmp.imaginary -> real ;T0[[I" imag;T@ I"();T@FI" Complex;TcRDoc::NormalClass00PKC]Z%2f-i.rinu[U:RDoc::AnyMethod[iI"/:ETI"Complex#/;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I"Performs division.;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [ I":Complex(2, 3) / Complex(2, 3) #=> ((1/1)+(0/1)*i) ;TI" ((900/1)+(0/1)*i) ;TI">Complex(-2, 9) / Complex(-9, 2) #=> ((36/85)-(77/85)*i) ;TI":Complex(9, 8) / 4 #=> ((9/4)+(2/1)*i) ;TI"RComplex(20, 9) / 9.8 #=> (2.0408163265306123+0.9183673469387754i);T: @format0: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0I"Acmp / numeric -> complex cmp.quo(numeric) -> complex ;T0[I" (p1);T@FI" Complex;TcRDoc::NormalClass00PKC]Hyy as_json-i.rinu[U:RDoc::AnyMethod[iI" as_json:ETI"Complex#as_json;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I"OReturns a hash, that will be turned into a JSON object and represent this ;TI" object.;T: @fileI"%ext/json/lib/json/add/complex.rb;T:0@omit_headings_from_table_of_contents_below000[I"(*);T@FI" Complex;TcRDoc::NormalClass00PKC]M to_json-i.rinu[U:RDoc::AnyMethod[iI" to_json:ETI"Complex#to_json;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I"oStores class name (Complex) along with real value r and imaginary value i as JSON string;T: @fileI"%ext/json/lib/json/add/complex.rb;T:0@omit_headings_from_table_of_contents_below000[I" (*args);T@FI" Complex;TcRDoc::NormalClass00PKC]tv to_s-i.rinu[U:RDoc::AnyMethod[iI" to_s:ETI"Complex#to_s;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I"#Returns the value as a string.;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [ I"6Complex(2).to_s #=> "2+0i" ;TI"9Complex('-8/6').to_s #=> "-4/3+0i" ;TI"8Complex('1/2i').to_s #=> "0+1/2i" ;TI">Complex(0, Float::INFINITY).to_s #=> "0+Infinity*i" ;TI":Complex(Float::NAN, Float::NAN).to_s #=> "NaN+NaN*i";T: @format0: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0I"cmp.to_s -> string ;T0[I"();T@FI" Complex;TcRDoc::NormalClass00PKC]WzwHHnumerator-i.rinu[U:RDoc::AnyMethod[iI"numerator:ETI"Complex#numerator;TF: privateo:RDoc::Markup::Document: @parts[ o:RDoc::Markup::Paragraph; [I"Returns the numerator.;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [I") 1 2 3+4i <- numerator ;TI" - + -i -> ---- ;TI"+ 2 3 6 <- denominator ;TI" ;TI"2c = Complex('1/2+2/3i') #=> ((1/2)+(2/3)*i) ;TI")n = c.numerator #=> (3+4i) ;TI"$d = c.denominator #=> 6 ;TI"2n / d #=> ((1/2)+(2/3)*i) ;TI"7Complex(Rational(n.real, d), Rational(n.imag, d)) ;TI"2 #=> ((1/2)+(2/3)*i) ;T: @format0o; ; [I"See denominator.;T: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0I" cmp.numerator -> numeric ;T0[I"();T@FI" Complex;TcRDoc::NormalClass00PKC]V+k44 to_f-i.rinu[U:RDoc::AnyMethod[iI" to_f:ETI"Complex#to_f;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I"IReturns the value as a float if possible (the imaginary part should ;TI"be exactly zero).;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [I"#Complex(1, 0).to_f #=> 1.0 ;TI"(Complex(1, 0.0).to_f # RangeError ;TI"'Complex(1, 2).to_f # RangeError;T: @format0: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0I"cmp.to_f -> float ;T0[I"();T@FI" Complex;TcRDoc::NormalClass00PKC]ژ real-i.rinu[U:RDoc::AnyMethod[iI" real:ETI"Complex#real;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I"Returns the real part.;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [I" Complex(7).real #=> 7 ;TI"Complex(9, -4).real #=> 9;T: @format0: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0I"cmp.real -> real ;T0[I"();T@FI" Complex;TcRDoc::NormalClass00PKC]鸚 %2d%40-i.rinu[U:RDoc::AnyMethod[iI"-@:ETI"Complex#-@;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I"#Returns negation of the value.;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [I" -Complex(1, 2) #=> (-1-2i);T: @format0: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0I"-cmp -> complex ;T0[I"();T@FI" Complex;TcRDoc::NormalClass00PKC].||%2b-i.rinu[U:RDoc::AnyMethod[iI"+:ETI"Complex#+;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I"Performs addition.;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [ I"1Complex(2, 3) + Complex(2, 3) #=> (4+6i) ;TI"3Complex(900) + Complex(1) #=> (901+0i) ;TI"4Complex(-2, 9) + Complex(-9, 2) #=> (-11+11i) ;TI"2Complex(9, 8) + 4 #=> (13+8i) ;TI"3Complex(20, 9) + 9.8 #=> (29.8+9i);T: @format0: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0I" cmp + numeric -> complex ;T0[I" (p1);T@FI" Complex;TcRDoc::NormalClass00PKC]Lhu real%3f-i.rinu[U:RDoc::AnyMethod[iI" real?:ETI"Complex#real?;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I"EReturns false, even if the complex number has no imaginary part.;T: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0I"CComplex(1).real? -> false Complex(1, 2).real? -> false ;T0[I"();T@FI" Complex;TcRDoc::NormalClass00PKC]%quo-i.rinu[U:RDoc::AnyMethod[iI"quo:ETI"Complex#quo;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I"Performs division.;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [ I":Complex(2, 3) / Complex(2, 3) #=> ((1/1)+(0/1)*i) ;TI" ((900/1)+(0/1)*i) ;TI">Complex(-2, 9) / Complex(-9, 2) #=> ((36/85)-(77/85)*i) ;TI":Complex(9, 8) / 4 #=> ((9/4)+(2/1)*i) ;TI"RComplex(20, 9) / 9.8 #=> (2.0408163265306123+0.9183673469387754i);T: @format0: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0I"Acmp / numeric -> complex cmp.quo(numeric) -> complex ;T0[I" (p1);T@FI" Complex;TcRDoc::NormalClass00PKC]abs-i.rinu[U:RDoc::AnyMethod[iI"abs:ETI"Complex#abs;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I"1Returns the absolute part of its polar form.;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [I"#Complex(-1).abs #=> 1 ;TI"$Complex(3.0, -4.0).abs #=> 5.0;T: @format0: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0I"5cmp.abs -> real cmp.magnitude -> real ;T0[[I"magnitude;T@ I"();T@FI" Complex;TcRDoc::NormalClass00PKC]^/{{%2d-i.rinu[U:RDoc::AnyMethod[iI"-:ETI"Complex#-;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I"Performs subtraction.;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [ I"1Complex(2, 3) - Complex(2, 3) #=> (0+0i) ;TI"3Complex(900) - Complex(1) #=> (899+0i) ;TI"1Complex(-2, 9) - Complex(-9, 2) #=> (7+7i) ;TI"1Complex(9, 8) - 4 #=> (5+8i) ;TI"3Complex(20, 9) - 9.8 #=> (10.2+9i);T: @format0: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0I" cmp - numeric -> complex ;T0[I" (p1);T@FI" Complex;TcRDoc::NormalClass00PKC]@vrectangular-i.rinu[U:RDoc::AnyMethod[iI"rectangular:ETI"Complex#rectangular;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I",Returns an array; [cmp.real, cmp.imag].;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [I"*Complex(1, 2).rectangular #=> [1, 2];T: @format0: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0I";cmp.rect -> array cmp.rectangular -> array ;T0[[I" rect;To;; [o; ; [I"GReturns a complex object which denotes the given rectangular form.;T@o; ; [I"*Complex.rectangular(1, 2) #=> (1+2i);T; 0;@;0[I" rect;T@ I"();T@FI" Complex;TcRDoc::NormalClass00PKC]|dl22rectangular-c.rinu[U:RDoc::AnyMethod[iI"rectangular:ETI"Complex::rectangular;TT: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I"GReturns a complex object which denotes the given rectangular form.;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [I"*Complex.rectangular(1, 2) #=> (1+2i);T: @format0: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0I"cComplex.rect(real[, imag]) -> complex Complex.rectangular(real[, imag]) -> complex ;T0[I"(p1, p2 = v2);T@FI" Complex;TcRDoc::NormalClass00PKC]4 %3d%3d-i.rinu[U:RDoc::AnyMethod[iI"==:ETI"Complex#==;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I"3Returns true if cmp equals object numerically.;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [ I"0Complex(2, 3) == Complex(2, 3) #=> true ;TI"0Complex(5) == 5 #=> true ;TI"0Complex(0) == 0.0 #=> true ;TI"1Complex('1/3') == 0.33 #=> false ;TI"0Complex('1/2') == '1/2' #=> false;T: @format0: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0I"&cmp == object -> true or false ;T0[I" (p1);T@FI" Complex;TcRDoc::NormalClass00PKC]";522%3c%3d%3e-i.rinu[U:RDoc::AnyMethod[iI"<=>:ETI"Complex#<=>;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I"?If +cmp+'s imaginary part is zero, and +object+ is also a ;TI"Ireal number (or a Complex number where the imaginary part is zero), ;TI"Fcompare the real part of +cmp+ to object. Otherwise, return nil.;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [ I"0Complex(2, 3) <=> Complex(2, 3) #=> nil ;TI"0Complex(2, 3) <=> 1 #=> nil ;TI".Complex(2) <=> 1 #=> 1 ;TI".Complex(2) <=> 2 #=> 0 ;TI".Complex(2) <=> 3 #=> -1;T: @format0: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0I"*cmp <=> object -> 0, 1, -1, or nil ;T0[I" (p1);T@FI" Complex;TcRDoc::NormalClass00PKC]%׮denominator-i.rinu[U:RDoc::AnyMethod[iI"denominator:ETI"Complex#denominator;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I"GReturns the denominator (lcm of both denominator - real and imag).;To:RDoc::Markup::BlankLineo; ; [I"See numerator.;T: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0I""cmp.denominator -> integer ;T0[I"();T@FI" Complex;TcRDoc::NormalClass00PKC][$$ rect-c.rinu[U:RDoc::AnyMethod[iI" rect:ETI"Complex::rect;TT: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I"GReturns a complex object which denotes the given rectangular form.;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [I"*Complex.rectangular(1, 2) #=> (1+2i);T: @format0: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0I"cComplex.rect(real[, imag]) -> complex Complex.rectangular(real[, imag]) -> complex ;T0[I"(p1, p2 = v2);T@FI" Complex;TcRDoc::NormalClass00PKC]"? hash-i.rinu[U:RDoc::AnyMethod[iI" hash:ETI"Complex#hash;TF: privateo:RDoc::Markup::Document: @parts[: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below000[I"();T@ FI" Complex;TcRDoc::NormalClass00PKC]A abs2-i.rinu[U:RDoc::AnyMethod[iI" abs2:ETI"Complex#abs2;TF: privateo:RDoc::Markup::Document: @parts[o:RDoc::Markup::Paragraph; [I"*Returns square of the absolute value.;To:RDoc::Markup::BlankLineo:RDoc::Markup::Verbatim; [I"$Complex(-1).abs2 #=> 1 ;TI"&Complex(3.0, -4.0).abs2 #=> 25.0;T: @format0: @fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0I"cmp.abs2 -> real ;T0[I"();T@FI" Complex;TcRDoc::NormalClass00PKB]+ \\ to_r-i.rinu[PKB],ľ phase-i.rinu[PKB]D inspect-i.rinu[PKB]2 fdiv-i.rinu[PKB](%2a%2a-i.rinu[PKB]eo@imaginary-i.rinu[PKC]ZB%2f-i.rinu[PKC]Hyy Eas_json-i.rinu[PKC]M xGto_json-i.rinu[PKC]tv CIto_s-i.rinu[PKC]WzwHH$Lnumerator-i.rinu[PKC]V+k44 Oto_f-i.rinu[PKC]ژ Rreal-i.rinu[PKC]鸚 T%2d%40-i.rinu[PKC].||U%2b-i.rinu[PKC]Lhu Xreal%3f-i.rinu[PKC]%VZquo-i.rinu[PKC]r]abs-i.rinu[PKC]^/{{_%2d-i.rinu[PKC]@vbbrectangular-i.rinu[PKC]|dl22:erectangular-c.rinu[PKC]4 g%3d%3d-i.rinu[PKC]";522{j%3c%3d%3e-i.rinu[PKC]%׮mdenominator-i.rinu[PKC][$$ orect-c.rinu[PKC]"? 6rhash-i.rinu[PKC]A Lsabs2-i.rinu[PK--3 Wu