I'm quite stuck on how to solve this using the Laurent expansion as the denominator is simply $z^3$ rather than something like $1-z$
separate question!
I'm not too sure how to solve this, I've found that for $|z|<1$ we have $$i\sum_{n=0}^\infty \bigg(\frac{z}{i}\bigg)^n$$ however, how would I find the summation for $|z|>0$?