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class Complex < Numeric
def self.polar(abs, arg = 0)
Complex(abs * Math.cos(arg), abs * Math.sin(arg))
end
def inspect
"(#{to_s})"
end
def to_s
"#{real}#{'+' unless imaginary < 0}#{imaginary}#{'*' unless imaginary.finite?}i"
end
def +@
self
end
def -@
Complex(-real, -imaginary)
end
def <=>(other)
return nil unless other.kind_of?(Numeric)
self.to_f <=> other.to_f
rescue
nil
end
def abs
Math.hypot imaginary, real
end
alias_method :magnitude, :abs
def abs2
real * real + imaginary * imaginary
end
def arg
Math.atan2 imaginary, real
end
alias_method :angle, :arg
alias_method :phase, :arg
def conjugate
Complex(real, -imaginary)
end
alias_method :conj, :conjugate
def fdiv(numeric)
Complex(real / numeric, imaginary / numeric)
end
def polar
[abs, arg]
end
def real?
false
end
def rectangular
[real, imaginary]
end
alias_method :rect, :rectangular
def to_c
self
end
def to_r
raise RangeError.new "can't convert #{to_s} into Rational" unless imaginary.zero?
Rational(real, 1)
end
alias_method :imag, :imaginary
Numeric.class_eval do
def i
Complex(0, self)
end
end
undef i
end
class Numeric
def to_c
Complex(self, 0)
end
end
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