Question

Q.1) Select and write the correct answer.
(10)
i) If w is a complex cube root of unity, then the value of
w99+w100+w 101 is
a) -1
b) 1
c)
d) 3​

Answer 1

Note that the cube roots of unity are the solution of x³=1.

It is solved by one equation. x³-1 can be factorized, because x-1=0 is a solution.

By factor theorem, we can divide by x-1. Next, by synthetic division, the given equation becomes:

(x-1)(x²+x+1)=0

Therefore, it is saying the solutions of x²+x+1=0. The discriminant is negative.

(By given condition ω³=1,) ω+ω²+1 is the given expression. Then, from above, we have proved that the value of ω²+ω+1 is equal to ...?