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U:RDoc::NormalClass[iI" Complex:ET@I" Numeric;To:RDoc::Markup::Document: @parts[o;;[?o: RDoc::Markup::Paragraph;[I"0A \Complex object houses a pair of values, ;TI"Ogiven when the object is created as either rectangular coordinates ;TI"!or polar coordinates.;To: RDoc::Markup::BlankLine S:RDoc::Markup::Heading:
leveli: textI" Rectangular Coordinates;T@o; ;[I"5The rectangular coordinates of a complex number ;TI"2are called the _real_ and _imaginary_ parts; ;TI"ssee {Complex number definition}[https://en.wikipedia.org/wiki/Complex_number#Definition_and_basic_operations].;T@o; ;[I"HYou can create a \Complex object from rectangular coordinates with:;T@o:RDoc::Markup::List:
@type: BULLET: @items[ o:RDoc::Markup::ListItem: @label0;[o; ;[I"IA {complex literal}[rdoc-ref:syntax/literals.rdoc@Complex+Literals].;To;;0;[o; ;[I"\Method Complex.rect.;To;;0;[o; ;[I"\\Method Kernel#Complex, either with numeric arguments or with certain string arguments.;To;;0;[o; ;[I".\Method String#to_c, for certain strings.;T@o; ;[I"PNote that each of the stored parts may be a an instance one of the classes ;TI"+Complex, Float, Integer, or Rational; ;TI"they may be retrieved:;T@o;;;;[o;;0;[o; ;[I"ASeparately, with methods Complex#real and Complex#imaginary.;To;;0;[o; ;[I"(Together, with method Complex#rect.;T@o; ;[I"@The corresponding (computed) polar values may be retrieved:;T@o;;;;[o;;0;[o; ;[I":Separately, with methods Complex#abs and Complex#arg.;To;;0;[o; ;[I")Together, with method Complex#polar.;T@S; ; i;
I"Polar Coordinates;T@o; ;[I"/The polar coordinates of a complex number ;TI"5are called the _absolute_ and _argument_ parts; ;TI"Xsee {Complex polar plane}[https://en.wikipedia.org/wiki/Complex_number#Polar_form].;T@o; ;[I"&In this class, the argument part ;TI"Bin expressed {radians}[https://en.wikipedia.org/wiki/Radian] ;TI"C(not {degrees}[https://en.wikipedia.org/wiki/Degree_(angle)]).;T@o; ;[I"BYou can create a \Complex object from polar coordinates with:;T@o;;;;[o;;0;[o; ;[I"\Method Complex.polar.;To;;0;[o; ;[I";\Method Kernel#Complex, with certain string arguments.;To;;0;[o; ;[I".\Method String#to_c, for certain strings.;T@o; ;[I"PNote that each of the stored parts may be a an instance one of the classes ;TI"+Complex, Float, Integer, or Rational; ;TI"they may be retrieved:;T@o;;;;[o;;0;[o; ;[I":Separately, with methods Complex#abs and Complex#arg.;To;;0;[o; ;[I")Together, with method Complex#polar.;T@o; ;[I"FThe corresponding (computed) rectangular values may be retrieved:;T@o;;;;[o;;0;[o; ;[I"[self.abs, self.arg].;To;;0;[o; ;[I"9#inspect: Returns a string representation of +self+.;To;;0;[o; ;[I".#real: Returns the real value for +self+.;To;;0;[o; ;[I"C#real?: Returns +false+; for compatibility with Numeric#real?.;To;;0;[o; ;[I")#rect (and its alias #rectangular): ;TI"7Returns the array [self.real, self.imag].;T@S; ; i;
I"Comparing;T@o;;;;[o;;0;[o; ;[I"]#<=>: Returns whether +self+ is less than, equal to, or greater than the given argument.;To;;0;[o; ;[I"@#==: Returns whether +self+ is equal to the given argument.;T@S; ; i;
I"Converting;T@o;;;;[ o;;0;[o; ;[I"D#rationalize: Returns a Rational object whose value is exactly ;TI"?or approximately equivalent to that of self.real.;To;;0;[o; ;[I"#to_c: Returns +self+.;To;;0;[o; ;[I"5#to_d: Returns the value as a BigDecimal object.;To;;0;[o; ;[I"L#to_f: Returns the value of self.real as a Float, if possible.;To;;0;[o; ;[I"O#to_i: Returns the value of self.real as an Integer, if possible.;To;;0;[o; ;[I"O#to_r: Returns the value of self.real as a Rational, if possible.;To;;0;[o; ;[I"6#to_s: Returns a string representation of +self+.;T@S; ; i;
I""Performing Complex Arithmetic;T@o;;;;[o;;0;[o; ;[I"=#*: Returns the product of +self+ and the given numeric.;To;;0;[o; ;[I">#**: Returns +self+ raised to power of the given numeric.;To;;0;[o; ;[I"9#+: Returns the sum of +self+ and the given numeric.;To;;0;[o; ;[I"@#-: Returns the difference of +self+ and the given numeric.;To;;0;[o; ;[I")#-@: Returns the negation of +self+.;To;;0;[o; ;[I">#/: Returns the quotient of +self+ and the given numeric.;To;;0;[o; ;[I"H#abs2: Returns square of the absolute value (magnitude) for +self+.;To;;0;[o; ;[I"G#conj (and its alias #conjugate): Returns the conjugate of +self+.;To;;0;[o; ;[I"P#fdiv: Returns Complex.rect(self.real/numeric, self.imag/numeric).;T@S; ; i;
I"Working with JSON;T@o;;;;[o;;0;[o; ;[I"3::json_create: Returns a new \Complex object, ;TI"1deserialized from the given serialized hash.;To;;0;[o; ;[I"A#as_json: Returns a serialized hash constructed from +self+.;To;;0;[o; ;[I"9#to_json: Returns a JSON string representing +self+.;T@o; ;[I"qThese methods are provided by the {JSON gem}[https://github.com/ruby/json]. To make these methods available:;T@o:RDoc::Markup::Verbatim;[I" require 'json/add/complex';T: @format0:
@fileI"complex.c;T:0@omit_headings_from_table_of_contents_below0o;;[ ;I"%ext/json/lib/json/add/complex.rb;T;0;0;0[ [U:RDoc::Constant[i I"I;TI"Complex::I;T: public0o;;[o; ;[I"Equivalent ;TI"$to Complex.rect(0, 1):;T@o;;[I"Complex::I # => (0+1i);T;0;@{;0@{@cRDoc::NormalClass0[ [[I"
class;T[[;[ [I"json_create;TI"%ext/json/lib/json/add/complex.rb;T[I"
polar;TI"complex.c;T[I" rect;T@[I"rectangular;T@[:protected[ [: private[ [I"
instance;T[[;[,[I"*;T@[I"**;T@[I"+;T@[I"-;T@[I"-@;T@[I"/;T@[I"<=>;T@[I"==;T@[I"abs;T@[I" abs2;T@[I"
angle;T@[I"arg;T@[I" as_json;T@[I" conj;T@[I"conjugate;T@[I"denominator;T@[I" fdiv;T@[I" finite?;T@[I" hash;T@[I" imag;T@[I"imaginary;T@[I"infinite?;T@[I" inspect;T@[I"magnitude;T@[I"numerator;T@[I"
phase;T@[I"
polar;T@[I"quo;T@[I"rationalize;T@[I" real;T@[I"
real?;T@[@@[I"rectangular;T@[I" to_c;T@[I" to_f;T@[I" to_i;T@[I" to_json;T@[I" to_r;T@[I" to_s;T@[;[ [;[ [ [U:RDoc::Context::Section[i 0o;;[ ;0;0[@{@~@~cRDoc::TopLevel