## i raised to the power of i

Remember the general rule

$a^b = e^{a \ ln(b)}$

Using this rule we can compute i raised to the power of i

$i^i = e^{i \ ln(i)} = e^{i i\pi/2} = e^{-\pi/2} = 0.207879576 \cdots$

remember that

$i=\sqrt{-1}$

$ln(1)=0$

$ln(i)=i\frac{\pi}{2}$

and $i i = \sqrt{-1} \sqrt{-1} = -1$