Class: Complex

Inherits:

Numeric

• Object
• NSObject
• NSValue
• NSNumber
• Numeric
• Complex

show all

Overview

Complex(1)           #=> (1+0i)
Complex(2, 3)        #=> (2+3i)
Complex.polar(2, 3)  #=> (-1.9799849932008908+0.2822400161197344i)
3.to_c               #=> (3+0i)

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)

Complex(1, 1) / 2    #=> ((1/2)+(1/2)*i)
Complex(1, 1) / 2.0  #=> (0.5+0.5i)

Constant Summary

I

Class Method Summary (collapse)

• + alloc
• + convert
• + polar

  Returns a complex object which denotes the given polar form.

• + rect

  Returns a complex object which denotes the given rectangular form.

• + rectangular

  Returns a complex object which denotes the given rectangular form.

Instance Method Summary (collapse)

• - *

  Performs multiplication.

• - **

  Performs exponentiation.

• - +

  Performs addition.

• - -

  Performs subtraction.

• - -

  Returns negation of the value.

• - /

  Performs division.

• - ==

  Returns true if cmp equals object numerically.

• - abs

  Returns the absolute part of its polar form.

• - abs2

  Returns square of the absolute value.

• - angle

  Returns the angle part of its polar form.

• - arg

  Returns the angle part of its polar form.

• - coerce

  :nodoc:.

• - complex?

  :nodoc:.

• - conj

  Returns the complex conjugate.

• - conjugate

  Returns the complex conjugate.

• - denominator

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

• - eql?

  :nodoc:.

• - exact?

  :nodoc:.

• - fdiv

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

• - hash

  :nodoc:.

• - imag

  Returns the imaginary part.

• - imaginary

  Returns the imaginary part.

• - inexact?

  :nodoc:.

• - inspect

  Returns the value as a string for inspection.

• - magnitude

  Returns the absolute part of its polar form.

• - marshal_dump

  :nodoc:.

• - marshal_load

  :nodoc:.

• - numerator

  Returns the numerator.

• - phase

  Returns the angle part of its polar form.

• - polar

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

• - quo
• - rationalize

  Returns the value as a rational if possible.

• - real

  Returns the real part.

• - real?

  Returns false.

• - rect

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

• - rectangular

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

• - to_f

  Returns the value as a float if possible.

• - to_i

  Returns the value as an integer if possible.

• - to_r

  If the imaginary part is exactly 0, returns the real part as a Rational, otherwise a RangeError is raised.

• - to_s

  Returns the value as a string.

• - ~

  Returns the complex conjugate.

Methods inherited from Numeric

#%, #+@, #, #ceil, #class, #div, #divmod, #dup, #floor, #i, #initialize_copy, #integer?, #modulo, #nonzero?, #remainder, #round, #scalar?, #singleton_method_added, #step, #to_c, #to_int, #truncate, #zero?

Methods included from Comparable

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

Methods inherited from NSNumber

#boolValue, #charValue, #compare:, #decimalValue, #descriptionWithLocale:, #doubleValue, #floatValue, #initWithBool:, #initWithChar:, #initWithDouble:, #initWithFloat:, #initWithInt:, #initWithInteger:, #initWithLong:, #initWithLongLong:, #initWithShort:, #initWithUnsignedChar:, #initWithUnsignedInt:, #initWithUnsignedInteger:, #initWithUnsignedLong:, #initWithUnsignedLongLong:, #initWithUnsignedShort:, #intValue, #integerValue, #isEqualToNumber:, #longLongValue, #longValue, numberWithBool:, numberWithChar:, numberWithDouble:, numberWithFloat:, numberWithInt:, numberWithInteger:, numberWithLong:, numberWithLongLong:, numberWithShort:, numberWithUnsignedChar:, numberWithUnsignedInt:, numberWithUnsignedInteger:, numberWithUnsignedLong:, numberWithUnsignedLongLong:, numberWithUnsignedShort:, #objCType, #shortValue, #stringValue, #unsignedCharValue, #unsignedIntValue, #unsignedIntegerValue, #unsignedLongLongValue, #unsignedLongValue, #unsignedShortValue

Methods inherited from NSValue

#getValue:, #initWithBytes:objCType:, #isEqualToValue:, #nonretainedObjectValue, #objCType, #pointerValue, #rangeValue, value:withObjCType:, valueWithBytes:objCType:, valueWithNonretainedObject:, valueWithPointer:, valueWithRange:

Methods inherited from NSObject

#!, #!=, #!~, #, #===, #=~, #Rational, #__callee__, #__method__, #__send__, #__type__, `, allocWithZone:, #autoContentAccessingProxy, autoload, autoload?, autorelease_pool, #awakeAfterUsingCoder:, binding, block_given?, caller, cancelPreviousPerformRequestsWithTarget:, cancelPreviousPerformRequestsWithTarget:selector:object:, catch, class, classFallbacksForKeyedArchiver, #classForCoder, #classForKeyedArchiver, classForKeyedUnarchiver, #clone, conformsToProtocol:, #copy, copyWithZone:, #dealloc, #define_singleton_method, description, display, #doesNotRecognizeSelector:, #dup, #enum_for, #equal?, #extend, fail, #finalize, format, #forwardInvocation:, #forwardingTargetForSelector:, framework, #freeze, #frozen?, getpass, gets, global_variables, #init, initialize, #initialize_clone, #initialize_copy, #initialize_dup, instanceMethodForSelector:, instanceMethodSignatureForSelector:, #instance_eval, #instance_exec, #instance_of?, #instance_variable_defined?, #instance_variable_get, #instance_variable_set, #instance_variables, instancesRespondToSelector:, isSubclassOfClass:, #is_a?, iterator?, #kind_of?, lambda, load, load_bridge_support_file, load_plist, local_variables, loop, #method, #methodForSelector:, #methodSignatureForSelector:, #methods, #mutableCopy, mutableCopyWithZone:, new, #nil?, open, p, #performSelector:onThread:withObject:waitUntilDone:, #performSelector:onThread:withObject:waitUntilDone:modes:, #performSelector:withObject:afterDelay:, #performSelector:withObject:afterDelay:inModes:, #performSelectorInBackground:withObject:, #performSelectorOnMainThread:withObject:waitUntilDone:, #performSelectorOnMainThread:withObject:waitUntilDone:modes:, print, printf, #private_methods, proc, #protected_methods, #public_method, #public_methods, #public_send, putc, puts, raise, rand, readline, readlines, #replacementObjectForCoder:, #replacementObjectForKeyedArchiver:, require, resolveClassMethod:, resolveInstanceMethod:, #respond_to?, #respond_to_missing?, select, #send, setVersion:, #singleton_methods, sprintf, srand, superclass, #taint, #tainted?, #tap, test, throw, #to_plist, trace_var, trap, #trust, #untaint, untrace_var, #untrust, #untrusted?, version

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)

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

Complex(10.0) / 3  #=> (3.3333333333333335+(0/1)*i)
Complex(10)   / 3  #=> ((10/3)+(0/1)*i)  # not (3+0i)

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

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

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

    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)

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