Question

 If 1, z_1, z₂, z₃ …… z_n–1 be the n^th roots of unity and ω be a non real complex cube root of unity then the product Π(ω -Zr) r ∈[r =1,n-1] can be equal to:

(A) 0 

(B) 1 

(C) – 1 

(D) 1 + ∞ 

Answer 1

Correct option (A,B,D)

Explanation:

(w – Z₁) (w – Z₂) (w – Z₃)….. (w – Z_n-1) = ?

If n is a multiple of 3, value can be zero as Z₁

can be w or w²

If n = 3K + 1 value is 1 

If n = 3K + 2 value is 1 + w