If z=12+i32z = \frac{1}{2} + \frac{i\sqrt{3}}{2}z=21+2i3, evaluate the infinite sum S=∑n=1∞zn2nS = \sum_{n=1}^{\infty} \frac{z^n}{2^n}S=∑n=1∞2nzn.
1−i33\frac{1-i\sqrt{3}}{3}31−i3
1+i37\frac{1+i\sqrt{3}}{7}71+i3
1+i33\frac{1+i\sqrt{3}}{3}31+i3
2+i35\frac{2+i\sqrt{3}}{5}52+i3