Returns the imaginary value for self:
Complex.rect(7).imag # => 0 Complex.rect(9, -4).imag # => -4
If self was created with polar coordinates, the returned value is computed, and may be inexact:
Complex.polar(1, Math::PI/4).imag # => 0.7071067811865476 # Square root of 2.
Returns the argument (angle) for self in radians; see polar coordinates:
Complex.polar(3, Math::PI/2).arg # => 1.57079632679489660
If self was created with rectangular coordinates, the returned value is computed, and may be inexact:
Complex.polar(1, 1.0/3).arg # => 0.33333333333333326
Returns the argument (angle) for self in radians; see polar coordinates:
Complex.polar(3, Math::PI/2).arg # => 1.57079632679489660
If self was created with rectangular coordinates, the returned value is computed, and may be inexact:
Complex.polar(1, 1.0/3).arg # => 0.33333333333333326
Returns the array [self.real, self.imag]:
Complex.rect(1, 2).rect # => [1, 2]
If self was created with polar coordinates, the returned value is computed, and may be inexact:
Complex.polar(1.0, 1.0).rect # => [0.5403023058681398, 0.8414709848078965]
Complex#rectangular is an alias for Complex#rect.
Returns the array [self.abs, self.arg]:
Complex.polar(1, 2).polar # => [1.0, 2.0]
See Polar Coordinates.
If self was created with rectangular coordinates, the returned value is computed, and may be inexact:
Complex.rect(1, 1).polar # => [1.4142135623730951, 0.7853981633974483]
Returns the conjugate of self, Complex.rect(self.imag, self.real):
Complex.rect(1, 2).conj # => (1-2i)
Returns the conjugate of self, Complex.rect(self.imag, self.real):
Complex.rect(1, 2).conj # => (1-2i)
Returns the Complex object created from the numerators of the real and imaginary parts of self, after converting each part to the lowest common denominator of the two:
c = Complex.rect(Rational(2, 3), Rational(3, 4)) # => ((2/3)+(3/4)*i) c.numerator # => (8+9i)
In this example, the lowest common denominator of the two parts is 12; the two converted parts may be thought of as Rational(8, 12) and Rational(9, 12), whose numerators, respectively, are 8 and 9; so the returned value of c.numerator is Complex.rect(8, 9).
Related: Complex#denominator.
Returns zero if self is positive, Math::PI otherwise.
Returns zero if self is positive, Math::PI otherwise.
Returns array [self, 0].
Returns array [self.abs, self.arg].
Returns a 2-element array containing two numeric elements, formed from the two operands self and other, of a common compatible type.
Of the Core and Standard Library classes, Integer, Rational, and Complex use this implementation.
Examples:
i = 2 # => 2 i.coerce(3) # => [3, 2] i.coerce(3.0) # => [3.0, 2.0] i.coerce(Rational(1, 2)) # => [0.5, 2.0] i.coerce(Complex(3, 4)) # Raises RangeError. r = Rational(5, 2) # => (5/2) r.coerce(2) # => [(2/1), (5/2)] r.coerce(2.0) # => [2.0, 2.5] r.coerce(Rational(2, 3)) # => [(2/3), (5/2)] r.coerce(Complex(3, 4)) # => [(3+4i), ((5/2)+0i)] c = Complex(2, 3) # => (2+3i) c.coerce(2) # => [(2+0i), (2+3i)] c.coerce(2.0) # => [(2.0+0i), (2+3i)] c.coerce(Rational(1, 2)) # => [((1/2)+0i), (2+3i)] c.coerce(Complex(3, 4)) # => [(3+4i), (2+3i)]
Raises an exception if any type conversion fails.
Returns self.
Raises an exception if the value for freeze is neither true nor nil.
Related: Numeric#dup.
Returns the remainder after dividing self by other.
Of the Core and Standard Library classes, only Float and Rational use this implementation.
Examples:
11.0.remainder(4) # => 3.0 11.0.remainder(-4) # => 3.0 -11.0.remainder(4) # => -3.0 -11.0.remainder(-4) # => -3.0 12.0.remainder(4) # => 0.0 12.0.remainder(-4) # => 0.0 -12.0.remainder(4) # => -0.0 -12.0.remainder(-4) # => -0.0 13.0.remainder(4.0) # => 1.0 13.0.remainder(Rational(4, 1)) # => 1.0 Rational(13, 1).remainder(4) # => (1/1) Rational(13, 1).remainder(-4) # => (1/1) Rational(-13, 1).remainder(4) # => (-1/1) Rational(-13, 1).remainder(-4) # => (-1/1)
Returns true if zero has a zero value, false otherwise.
Of the Core and Standard Library classes, only Rational and Complex use this implementation.
Returns true if self is greater than 0, false otherwise.
Returns true if self is less than 0, false otherwise.
Returns zero.
Returns self.
Returns the numerator.
Compares self.downcase and other_string.downcase; returns:
-1 if other_string.downcase is larger.
0 if the two are equal.
1 if other_string.downcase is smaller.
nil if the two are incomparable.
Examples:
'foo'.casecmp('foo') # => 0 'foo'.casecmp('food') # => -1 'food'.casecmp('foo') # => 1 'FOO'.casecmp('foo') # => 0 'foo'.casecmp('FOO') # => 0 'foo'.casecmp(1) # => nil
See Case Mapping.
Related: String#casecmp?.
Returns true if self and other_string are equal after Unicode case folding, otherwise false:
'foo'.casecmp?('foo') # => true 'foo'.casecmp?('food') # => false 'food'.casecmp?('foo') # => false 'FOO'.casecmp?('foo') # => true 'foo'.casecmp?('FOO') # => true
Returns nil if the two values are incomparable:
'foo'.casecmp?(1) # => nil
See Case Mapping.
Related: String#casecmp.