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!

Definition...
$$
a^b = \exp(b\log a)
$$
Of course "$\log$" is the natural logarithm.
And it is multi-valued.  Suppose we choose "principal values" as
$$
\log(-1) = i\pi,
\\
\log i = \frac{i\pi}{2}
$$
then what do we get?  Can you compute the values for $i^i$ and $(-1)^{2i}$ yourself?  
And what happens if you choose some value other than these principal values?
