If we have a natural $n$ (not $0$), and a prime $p$, is it possible to calculate
$$a^{n i} \mod p$$
where $i$ is the imaginary number $\sqrt{-1}$?
SOME THOUGHTS
Knowing that $a^{i \cdot i} = a^{-1}$ may help. Also, modulo a prime $p$, we of course have $e^{2 i \pi/(p-1)}$, and all integer multiples of that power.
Don't ask if it's possible to calculate, ask what the result could possibly mean. "$\ldots \mod p$" implies membership in the field of integers mod $p$, or at least some vector space over that field. Your $a^{ni}$ exists in the complex numbers, the wrong field entirely.