Suppose A is a complex number and n∈N, such that An = (A + 1)n = 1, then the least value of n is

Let A = x + iy. Given,|A|=1⇒x2+y2=1and |A+1|=1⇒(x+1)2+y2=1⇒     x=−12 and y=±32⇒     A=ω or ω2⇒     (ω)n=(1+ω)n=−ω2nTherefore, n must be even and divisible by 3.