COMPLEX NOS.

You should make it a habit to first search the site if the problems you are going to ask has been already discussed. This question for instance has been discussed a number of times earlier.

Anyway
i^i = (e^{i(2n\pi + \frac{\pi}{2})})^i=e^{i^2(2n\pi + \frac{\pi}{2})}=e^{-(2n\pi + \frac{\pi}{2})}
which is a positive real number. (Here n is an integer)

i=e^\pi/2 i

i^i=(e^\pi/2 i)^i

=e^\pi/2i^2
e^-\pi /2

arg =0

is it correct