The n roots of unity

Suppose you want the n roots of -1

e(int)= -1

t= pi/n cos( pi/n)+isin(pi/n) is one root to get the others divide 2pi/n and succesively add multiples of 2pi/n to pi/n to get the n roots

eg the 4 roots of -1 you use pi/4 ,3pi/4 etc in cos(t)+isin(t)

To get the n roots of 1

we have of course 0, then add 2pi/n to get the others

eg the four roots of unity are 0,pi/2,pi,3pi/2, correspondingly 1,i,-1,-1