UPSC NDA I 2017 Mathematics Solved Paper

Concept:The cube roots of unity satisfy $\omega^3 = 1$ and $1 + \omega + \omega^2 = 0$.Explanation:The expression is $(1 + \omega)(1 + \omega^2)(1 + \omega^3)(1 + \omega + \omega^2)$.For cube roots of unity, the sum $1 + \omega + \omega^2$ equals zero.This is the last factor in the product.Any product multiplied by zero is zero.Therefore, the entire expression evaluates to zero regardless of the other factors.(Note that $\omega^3 = 1$, so $1 + \omega^3 = 2$, but it does not affect the result.)Answer:The value is $0$, which corresponds to option C.