Let z=a( cos (π/5)+i sin (π/5)), a ∈ R ,|a|

Question

Let z=a( cos (π/5)+i sin (π/5)), a ∈ R ,|a|<1, then S=z2015+z2016+z2017+ ldots equals (A) (a2015/z-1) (B) (a2015/1-z) (C) (z2015/1-a) (D) (z2015/a-1)

Tardigrade Admin · Accepted Answer

Solution: We have |z|=|a|<1, thus S =(z2015/1-z) text But z2015 =a2015[ cos (403 π)+i sin (403 π)]=-a2015 ∴ S =(a2015/z-1)

Q. Let $z = a (cos \frac{π}{5} + i sin \frac{π}{5}), a \in R, ∣ a ∣ < 1$ , then $S = z^{2015} + z^{2016} + z^{2017} + \dots$ equals