Problem 4: Recall that power functions are defined by $z^c = e^{c \log(z)}$. In this exercise, we compute all
power functions by using the branch $(0 \le \theta < 2\pi)$ for $\log(z)$.
(a) For $z = -i$ and $c = i$, compute the values of $(z^c)^2$, $(z^2)^c$, and $z^{(2c)}$.
(b) With the notation as in (a), which of these are true or false?
$(z^c)^2 = (z^2)^c$,
$(z^c)^2 = z^{(2c)}$,
$(z^2)^c = z^{(2c)}$.
