1. The problem statement, all variables and given/known data Let z1, .... zn be the set of n distinct solutions to the equation zn = a where a is a complex number. (a) By considering distinct solutions as the sides of a polygon in an Argand diagram show that these sum to zero. (b) Hene find the sum of the squares of these solutions. For the case n = 5 sketch the polygon traced out by these successive squared values in the Argand plane. 3. The attempt at a solution Of course this can be easily solved by doing summation of geometric series, but this isn't a typical question... I managed to show that the sum of sides = 0 algebraically. This can be shown by using vectors as well (red arrows) that starting from point z1 you will arrive back at z1, implying the overall change = 0. But, how do i relate each side of the polygon to one solution? Is there a bijection somewhere?