Question

how to prove i^i is a real number?

Answer 1

Use ln(-1)

Answer 2

\[i^i\] first write
\[i=e^{\frac{\pi}{2}i}\] and then raise it to the ith power

Answer 3

arnab

Answer 4

you get
\[e^{-\frac{\pi}{2}}\]

Answer 5

beautiful!

Answer 6

thnx
and only one cup of coffee

Answer 7

cant get the probability question though

Answer 8

Let i^i = e^x ->

i ln i = x

i ln (sqrt(-1)) = x

i/2 ln -1 = x but since ln -1 = ipi

x = -pi/2