From: Martin DeMello <martindemello@...>
Date: 2003-02-06T07:48:50+09:00
Subject: Re: Error in Complex

Daniel Carrera <dcarrera@math.umd.edu> wrote:
> 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?

Nothing, really.

Remember that z^x is multivalued in general - but the primary value is
the one obtained when -pi/2 <= theta <= pi/2

(we have z = r exp(i theta) = r exp i(theta + 2npi)
z ^ x = r^x exp(ixtheta + i2nxpi) = r^x [exp(ixtheta) * exp(i 2npi x)]

and for noninteger x, the second term is not 1. In your case, it's 
exp(4/3 i pi) which accounts for the difference)

martin