N-th roots of complex numbers?



On 2013-10-01, John Lapeyre <lapeyre.math122a at gmail.com> wrote:

> I see three possible interpretations of this example
>   (are there more ?) :
>
>   1. (-1)^(1/6) means one particular root of z^6=-1
>     (e.g. the principal root). solve gave the
>     correct answer. But perhaps solve should have
>     applied rectform itself.
>
>   2. the meaning of (-1)^(1/6) depends on the context.
>     eg if it appears at the top-level of expressions
>     in a list of three elements, then it means
>     the same root in each case, maybe a specific
>     root. This is obviously problematic.
>
>   3. (-1)^(1/6) means any one of the the six roots,
>     or maybe all of them. It's up to the user to
>     decide. In this case, solve gave an incorrect answer
>     and this is a bug in solve.

I think it's a bug in solve that the result is ambiguous.
If we can't even solve a simple equation unambiguously, who knows what
will happen in complicated problems.

best

Robert Dodier