TITLE: How to calculate $i^i$
QUESTION [9 upvotes]: I've been struggling with this problem, actually I was doing a program in python and did 
1j ** 1j(complex numbers) (In python a**b = $a^b$ ) 
and found out the answer to be a real number with value $0.2079$, How to calculate this value of $i^i$?

REPLY [4 votes]: $e^{i\pi} = -1$
$i = \sqrt{e^{i\pi}}$
$i^i = e^{-\frac{\pi}{2}}$
I just wanted to point out the derivation!