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)²(ω²)

= ω⁶

= 1

Hence option (1) is the answer.