From: "Hal E. Fulton" <hal9000@...>
Date: 2003-02-06T07:19:00+09:00
Subject: Re: Error in Complex

----- Original Message ----- 
From: "Martin DeMello" <martindemello@yahoo.com>
Newsgroups: comp.lang.ruby
To: "ruby-talk ML" <ruby-talk@ruby-lang.org>
Sent: Wednesday, February 05, 2003 4:08 PM
Subject: Re: Error in Complex


> Daniel Carrera <dcarrera@math.umd.edu> wrote:
> > Hello,
> > 
> > There seems to be a problem in Complex.  It gets (-i)^2/3 wrong.
> > 
> > 2/3
> > i    =  1/2 + sqrt(3)/2
> > 
> >   2/3
> > (-i) = - 1
> 
> -i = exp(-i * pi/2)
> (-i)^(2/3) = (1)^2/3 * exp(-i * pi/2 * 2/3)
>            = exp(-i * pi/3)
>    = cos(pi/3) - i sin(pi/3)
>    = 1/2 - sqrt(3)/2

OK, I admit I'm showing my ignorance here.
How do you reconcile that with:

(-i)**(2/3.0) 
((-i)**2)**3.0)
(-1)**3.0
-1

??
Hal