Question

if w is a completes root of unity such that x=a+b,y=aw+bw²andz=aw²+bw,a,b€r then prove that
1 . x+y+z=0
2. x³+y³+z³=3(a³+b³)​

Answer 1

Step-by-step explanation:

1.L.H.S=x+y+z=a+b+aw+b(w^2)+a(w^2)+bw

=a(1+w+w^2)+b(1+w+w^2)

=a×0+b×0

=0=R.H.S(proved)