# Rotations in Complex plane

The cyclic group $C_{n}$ is the group of n rotations that maps a regular n-gon onto itself. These rotations correspond to multiplying C by which n complex numbers?
The cyclic group $C_{n}$ is the group of n rotations that maps a regular n-gon onto itself. These rotations correspond to multiplying C by which n complex numbers?
If $\displaystyle\varsigma = \exp \left( {\frac{{2\pi i}}{n}} \right)$ then the complex numbers $\varsigma^k,~k=0,1,\cdots n-1$ will work.