I've done part a) I just simply cubed z and expanded, then seperated real and imaginary. I assume this is all that's needed?
For part b) I have no idea how to do it.
I doubt they are talking about the Cauchy Principal value so
what I'm going to assume they mean in (b) is simply the value of $\displaystyle \small 2^{i+1} \text { for } (0 \leq \theta <2\pi)$
$\displaystyle \small 2^{i+1}=e^{(i+1)ln(2)}$
$\displaystyle \text{You can probably come up with } z=r e^{i\theta}\text{ for that.}$