Mike Valenzuela wrote:
> Then taking a root produces multiple answers:
> ( r*exp(%i*theta + 2*n*%i*%pi) )^(z) = r^(z) * exp(%i*theta*z +
> 2*n*%i*%pi*z),
> where r^z only has to worry about the "simple case" returning a real
> positive value. Then the trick is to run through as many integers of n as
> we care about. If z is rational number, then an finite set of n covers all
> possible outputs. I believe (although I ask someone fact check this), if z
> is irrational, then there are infinitely many answers.
>
This results from Kronecker density theorem (which is refined by Weyl uniform
density theorem) of the points multiples on an irrational on the circle. See
for example last chapter of Hardy and Wright.
--
Michel Talon