Ki Song
Posts:
371
Registered:
9/19/09


Re: What's the geometry meaning of i^i ?
Posted:
Jul 27, 2012 2:25 PM


On Friday, July 27, 2012 11:19:26 AM UTC4, Ken S. Tucker wrote: > Butch Malahide wrote: > > > On Jul 27, 12:22 am, "Ken S. Tucker" <dynam...@rocketmail.com> wrote: > > >> Unit length is one solution. (i^i)^4 =1 , 1^(1/4)=1. > > > > > > What did you mean by "(i^i)^4 =1"? Must be a typo, but a typo for > > > what?? > > > > If memory serves, > > (i^i)^2 = i^2i= (1)^i , (1)^2i = 1^i = 1 = (i^i)^4 .
The rules of exponent do not expend to exponentiation by complex numbers.
> > > > I assume 1^(anything) = 1.
This is not true when the exponent is not a real number.
> > > > Now 1^(1/4) = i^i = 1. > > > > Hows that?
I think you need to think about what it means to "exponentiate." It's not such an obvious thing.
> > Ken

