From: Daniel Carrera <dcarrera@...>
Date: 2003-02-06T07:20:33+09:00
Subject: Re: Error in Complex

Martin,

I can see that your answer is right.  Perhaps you can show me what I'm 
doing wrong.  My colleagues and I can't figure it out:

   
-i = exp(i*3*pi/2)

   2/3
(-i)  = exp(i * 3pi/2 *(2/3))
      = exp(i * pi)
      = -1

What am I doing wrong?

On Thu, Feb 06, 2003 at 07:08:37AM +0900, Martin DeMello wrote:
> 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
> 
> martin
> 

-- 
Daniel Carrera
Graduate Teaching Assistant.  Math Dept.
University of Maryland.  (301) 405-5137