Question

If 1, w, w2 are the cube roots of unity, find (2 + w+ w2)6+ (3 +w+w2)6

Answer 1

Step-by-step explanation:

If 1, w and w^2 are cube roots of unity, then 1 + w + w^2 = 0 => w + w^2 = (-1)

So, (2 + w+ w^2)^6 + (3 +w+w^2)^6

= (2-1)^6 + (3-1)^6

= 1^6 + 2^6

= 1 + 64 = 65 answer.

If it's (2 + w+ w^2)6 + (3 +w+w^2)6

then = (2-1)6 + (3-1)6

= 1 × 6 + 2 × 6 = 6 + 12 = 18 answer.