Skillful Observer » Maths WTF?

Maths WTF?

You know complex numbers right? Where a
complex number
$i=sqrt(-1)$
Now what happens if you want to know the outcome of
$sqrt(-1)^{\tiny{\sqrt(-1)}}=??$

This is where the fun begins. Euler gave us this great tool
$e^{i \pi} = -1$
which becomes
$e^{\frac{i \pi}{2}}=-{1}^{1/2}$
simpyfies to
$e^{{\frac{i \pi}{2}}}=i$
and because the logarithm is valid for complex numbers
$\frac{i \pi}{2}=ln(i)$

Because power works a litte different for complex numbers
$z^\omega=e^{\omega \ln(z)}$
you end up with
$i^{i}=e^{i ln(i)}$
and we know that
$i\frac{\pi}{2}=ln(i)$