Question

If w is a non real cube root of unity then the value of 

1.(2-w)(2-w²)+2.(3-w)(3-w²)+............+(n-1)(n-w)(n-w²) is 

(a) real

(B) {n²(n-1)/4} -n+1

(C) {n(n+1)/2}² -n

(D) not real

Answer 1

Correct answer is option (C) i.e {n(n+1)/2}² -n

Explanation:

Let S = 1.(2-w)(2-w²)+2.(3-w)(3-w²)+............+(n-1)(n-w)(n-w²)