Question

- may be proving that an imaginary number on an imaginary power is real ?

for example : i^(1/i)

or why not ?

Answer 1

\(\large{z_1 = re^{i\theta}}\)
\(z_2 = a+ ib\)

\(\Large {z_1^{z_2}}\)

\(\Large {\left(re^{i\theta}\right)^{a+ib}}\)

you can simplify it further to find out the conditions for it to be real/imaginary