sub Cmp_string
{
    #get the object
    my $a = shift;
    
    #figure out what sign to put between the real
    #   and imaginary part. I do this so we don't get
    #   something like '3 + -5I', although it fairly 
    #   irrelevant
    my $sign = ($a->Imag > 0) ? " + " : " - ";
    
    #return a string that looks like '3 - 5I'
    return $a->Real.$sign.abs($a->Imag)."I";
}

sub Cmp_add
{
    #get the calling object;  $a is always the Complex object, it
    #   does not matter if we call '$x + 2' or '2 + $x' or 
    #   '$x + $y' ... this $a will always be $x.
    my $a = shift;
    
    #get the second object, either a number or an object
    my $b = shift;
    
    #if $b is not a Complex object do the simple math
    unless( $b->isa( 'Complex' ) )
    {
        #return a new Complex object after doing the simple
        #   arithmetic
        return new Complex( $a->Real + $b, $a->Imag );
    }
    
    #return a new Complex object after doing the 'complex'
    #   arithmetic    
    return new Complex($a->Real+$b->Real, $a->Imag+$b->Imag); 
}

sub Cmp_multiply
{
    #get the calling object;  $a is always the Complex object, it
    #   does not matter if we call '$x * 2' or '2 * $x' or 
    #   '$x * $y' ...  this $a will always be $x.
    my $a = shift;

    #get the second object, either a number or an object
    my $b = shift;

    unless( $b->isa( 'Complex' ) )
    {   
        #return a new Complex object after doing the simple
        #   arithmetic
        return new Complex( $a->Real * $b, $a->Imag * $b);
    }
    
    #figure out the new real and imaginary parts.  Good'ol
    #   FOIL method anybody?
    my $real = ($a->Real * $b->Real) + ($a->Imag * $b->Imag * -1);
    my $imag = ($a->Real * $b->Imag) + ($a->Imag * $b->Real); 
    
    #return a new Complex object after doing the 'complex'
    #   arithmetic    
    return new Complex($real, $imag);
}