question_answer

If \[\omega =\frac{-1+\sqrt{3}i}{2}\]then \[{{(3+\omega +3{{\omega }^{2}})}^{4}}\]= [Karnataka CET 2004; Pb. CET 2000]

A) 16

B) -16

C) 16 \[\omega \]

D) 16\[{{\omega }^{2}}\]

Correct Answer: C

Solution :

\[{{(3+\omega +3{{\omega }^{2}})}^{4}}=[{{(3+3{{\omega }^{2}}+\omega )}^{4}}]\] \[={{[\,3\,(1+{{\omega }^{2}})+\omega ]}^{4}}\]\[={{[3(-\omega )+\omega ]}^{4}}\] .