Hint: The cube roots of unity can be defined as the numbers which when raised to the power of 3 gives the result as 1 i.e., in simple words, the cube root of unity is the cube root of 1 i.e., 3√1. To show that (2−w)(2−w2)(2−w10)(2−w11)=49 hence, consider the properties of the cube root to obtain the given equation

Step-by-step explanation:Correct option is

D

−128ω

2

Since w is the imaginary cube root of unity

w

3

=1 and

1+w+w

2

=0 …(i)

Hence

(1+w−w

2

)

7

=((1+w)−w

2

)

7

=(−w

2

−w

2

)

7

…from i

=(−2w

2

)

7

=−128w

14

=−128w

12

.w

2

=−128(w

3

)

4

.w

2

=−128w

2

…since w

3

=1.

Answer:Hint: The cube roots of unity can be defined as the numbers which when raised to the power of 3 gives the result as 1 i.e., in simple words, the cube root of unity is the cube root of 1 i.e., 3√1. To show that (2−w)(2−w2)(2−w10)(2−w11)=49 hence, consider the properties of the cube root to obtain the given equation