Question

Can the imaginary number i be raised to the power of a fractional number, say 1/2 or 1/4?

Answer 1

in theory, why not?

Answer 2

Please elaborate. How would I be able to do this?

Answer 3

understand that
\[b^x=e^{x\ln(b)}\] would help

Answer 4

the answer is not unique for complex numbers
\[i^{\frac{1}{2}}=\sqrt{i}\] or a number whose square is \(i\)
there are two such numbers