Question

if w is a cube root of unity then (1+w)^3-(1+w^2)^3=​

Answer 1

Answer:

The answer is 0 (zero).

Step-by-step explanation:

(a+b)^3 = a3 + b3 + 3ab(a+b)

Given question is(1+w)^3-(1+w^2)^3

= 1 + w3 + 3*1*w(1+w) -(1+ w6+ 3*w2(1+w2))

here w3=1 and w6= (w3)^2

so w6= (1)^2 =1

= 1+1+3*w+3*w2-(1+1+3*w2+3*w4)

= 1+1+3*w+3*w2-(2+3*w2+3*w)

here w4 = w3*w and w3=1

so, w4 = w.

= 2+3*w+3*w2-(2+3*w2+3*w)

= 2+3*w+3*w2 -2 -3*w2 -3*w

= 0

Hope you are satisfied with the solution.