ComplexNumber data type

ComplexNumber.rb

class ComplexNumber
  attr_accessor :re, :im

  def initialize(re, im)
    # when ComplexNumber.new is called, initialize 
    # is run after the object is instantiated
    @re = re
    @im = im
  end

  def +(z)
    sum = ComplexNumber.new @re + z.re, @im + z.im
  end

  def *(z)
    prod = ComplexNumber.new @re*z.re - @im*z.im, @im*z.re + @re*z.im
  end

  def conjugate
    # complex conjugate
    cong = ComplexNumber.new @re, -@im
  end

  def to_s
    # the to_s function outputs a string automatically, for example:
    # suppose z is an object of type ComplexNumber, then   
    # puts z     will implicitly call z.to_s and then output the result
    output = ""
    if @im >= 0
      output = "#{@re} + #{@im}i"
    else
      output = "#{@re} - #{-1*@im}i"
    end 
    output # return the string
  end
end

# example usage of ComplexNumber objects
w = ComplexNumber.new -1, -1     # => -1 - 1i
z = ComplexNumber.new 3, 1       # => 3 + 1i
puts "w + z = #{w + z}"          # => 2 + 0i
puts "w * z = #{w * z}"          # => -2 - 4i
puts "the complex conjugate of #{w} is #{w.conjugate}"
puts "the product of a complex number and it's conjugate is always real:"
puts "\tw * w.conjugate = #{w*w.conjugate}"
puts "\tz * z.conjugate = #{z*z.conjugate}"