I have a question......

$\text{For those who don't know what is imaginary number: }\\i=\sqrt{-1}$

We know that $i^i = e^{-\pi/2}$

and

$e^{i\pi} + 1 = 0$, the famous Euler's formula.

We can derive from the Euler's formula that $\ln(-1) = -i\pi$

Therefore $\ln(i) = \ln((-1)^{1/2})=\dfrac{1}{2} \ln(-1)=-\dfrac{i\pi}{2}$

We take the exponential of both sides:

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

Raise to the power i both sides:

$i^i = e^{-(-\pi/2)}=\dfrac{1}{i^i}$

So that$(i^i)^2 = 1$

Therefore we get $i^i = \pm 1$(What is this?????????)

I am so confused, am I wrong?