Math Help - Can you raise stuff to the power of "i" ?

1. Can you raise stuff to the power of "i" ?

Can you raise variables to the power of "i"--the imaginary unit--just as you would raise them to the power of a real number?

For example, can I take this equation...

$1=ax^{2}$

...and do this...

$1^i=(ax^{2})^i$

...resulting in...

$1=a^i x^{2i}$

Or is that against the rules?

2. You can raise any number to any power you like, but you should convert everything to exponential polar form, makes exponentiation much easier...

E.g. $1^i = (1 + 0i)^i$

$= (\cos{2\pi n} + i\sin{2\pi n})^i$, where $n$ is an integer

$= (e^{2\pi n i})^i$

$= e^{2\pi n i^2}$

$= e^{-2\pi n}$.