Question

if 1,w,w^2 are the cube roots of unity then prove the following (1+w)(1+w^2)(1+w^7)(1+w^8)=1​

Answer 1

Step-by-step explanation:

(1+w)(1+w^8)(1+w^2)(1+w^7)

=(1+w){1+(w^3)^2.w^2}(1+w^2). {1+(w^3)^2.w}

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

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

={(1+w)(1+w^2)}^2

={1+w^2+w+w^3}^2

=(1+w+w^2+1)^2 [since,1+w+w^2=0]

=(2-1)^2

=1²

=1