Question #3bc5d

1 Answer
Dec 16, 2016

The answer is 16omega.

Explanation:

Since, root(3)(1)=omega,
So, omega^3=1.-----(1).

:.omega^3-1=0
:.(omega-1)(omega^2+omega+1)=0

So, either first term is zero, or the second term is zero.

But, if omega-1=0, omega=1, which is not true.

So, omega^2+omega+1=0.
:.omega^2+1=-omega.----(2).

Now, (3+omega+3omega^2)^4
={omega+3(omega^2+1)}^4
={omega+3(-omega)}^4 ----[From (2)].
=(omega-3omega)^4
=(-2omega)^4
=16omega^4
=16omega^3xxomega
=16xx1xxomega ----[From (1)].
=16omega. (Answer).

Hope it Helps :)