# Rotations in Complex plane

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• March 17th 2011, 01:00 PM
meggnog
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?
• March 17th 2011, 01:17 PM
Plato
Quote:

Originally Posted by meggnog
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.