Question

if 1,w, w^2 are the cube roots of Unity then (3+5w+3w^2)^2 is a)6 b)8 c)12 d)4 ​

Answer 1

Answer:

Given,

1+3w+w

2

+(1+3−w

2

)

4

=1+3w+w

2

+(−w

2

+4)

4

=1+3w+w

2

+w

8

−16w

6

+96w

4

−256w

2

+256

=w

8

−16w

6

+96w

4

−255w

2

+3w+257

=w

2

−16+96w−255w

2

+3w+257

=241−256w

2

+99w