Question

What does iota(i) raised to the power iota(i) equals to ?
that is
i ^ i = ?

Answer 1

We know that $cos x + i.sinX = e^{i.X}$

Now lets take a clean and easy value of x which clears out all values except for the one which has i in it
So lets take $x = \frac{\pi}{2}$

Now we get

$i = e^{i \frac{ \pi }{2} }$

Raise both sides to The power of i 

$i^i = {e^{i \frac{ \pi }{2} }}^i$

$i ^i= e^{i \frac{ \pi }{2} .i}$

$i ^i= e^{- \frac{ \pi }{2} }$

Punch the value into a scientific calc

$i ^i= e^{- \frac{ \pi }{2} }= 0.207<span>$