complex analysis - What's $i^e$, and why is there an imaginary part?

I am not sure if this is a straightforward question, since I am not familiar with complex analysis.

$i^e = e^{(i*π/2)*e} = (e^{iπ})^{e/2} = (-1)^{e/2}$

I think that's somewhat right, but when I put this into a calculator an imaginary part also comes out.

Is this because of $e$?