From: "Hal E. Fulton" <hal9000@...>
Date: 2003-02-06T07:24:40+09:00
Subject: Re: Error in Complex

----- Original Message ----- 
From: "Hal E. Fulton" <hal9000@hypermetrics.com>
To: "ruby-talk ML" <ruby-talk@ruby-lang.org>
Sent: Wednesday, February 05, 2003 4:19 PM
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

Sorry to amend my post, but what I meant 
of course was:
(-i)**(2/3.0)
((-i)**2)**(1/3.0)
(-1)**(1/3.0)
-1

Hal