Checkout JEE MAINS 2022 Question Paper Analysis : Checkout JEE MAINS 2022 Question Paper Analysis :

# If 1, w and w^2 are the cube roots of unity, then , is equal to (1+w)(1+ w^2)(1 +w^4)(1+ w^8) is equal to(1) 1 (2) 0 (3) w^2 (4) w

Given 1, ω and ω2 are the cube roots of unity.

1+ω+ω2 = 0

1+ω = -ω2

1+ω2 = -ω

(1+ω)(1+ ω2)(1+ω4)(1+ω8) = (1+ω)(-ω)(1+ω)(1+ω2)

= (1+ω)2(-ω-ω3)

= (1+ω)2(-ω-1)

= (-ω2)22)

= ω6

= 1

Hence option (1) is the answer.