Exercise $6$:

If $i=\sqrt[\phantom{2}]{-1},$ the complex number, the exact numerical value of

a$)e^i+{\displaystyle \underset{k=1}{\overset{}{}}}\frac{1}{2^k}=$

b$)e^i+(\frac{2}{3}+\frac{2}{9}+\frac{2}{27}+$cdots$)=$

c$)e^{i\frac{}{2}}+(\frac{2}{3}+\frac{4}{9}+\frac{8}{27}+$cdots$)=$

d$)e^i+(\frac{4}{3}+\frac{4}{9}+\frac{4}{27}+\frac{4}{81}+\frac{4}{243}+$cdots$)=|x||$

e$)e^{i\frac{}{4}}+{\displaystyle \underset{k=1}{\overset{}{}}}\frac{1}{3^k}=$

Do part d only please!