What are values of $2^i, i^i$ and $(-1)^{2i}$? Is the value of $2^i$ $\cos(\ln(2)) + i\;\sin(\ln(2))$? But I don't know how to calculate the value of $i^i$? And for the last one, is it the same as $1^i$? Thank you guys so much!

$e^{it} = \cos t + i \sin t$
$2 = e^{\ln2}$
$2^i = e^{i\ln2} = \cos (\ln 2) + i \sin (\ln 2)$
$i = e^{\frac \pi2 i}, i^i = e^{-\frac \pi2}$
$-1 = e^{ \pi i}, (-1)^{2i} = e^{-2\pi}$
