Question

Prove that $1+{\omega }^n+{\omega }^{2n}=3$ when n is the multiple of 3

Answer 1

since n is the mulitiple of 3 we have${\omega }^n=1and{\omega }^{2n}=1$
Hence $1+{\omega }^n+{\omega }^{2n}=1+1+1=3.$