Tuesday, May 17, 2011

de Moivre's formula

de Moivre's formula 
From http://en.wikipedia.org/wiki/De_Moivre's_formula:

By expanding the left hand side and then comparing the real and imaginary parts under the assumption that x is real, it is possible to derive useful expressions for cos (nx) and sin (nx) in terms of cos x and sin x. Furthermore, one can use a generalization of this formula to find explicit expressions for the nth roots of unity, that is, complex numbers z such that zn = 1.