Complex Numbers And Quadratic Equations question 293
Question: If $ \omega =\frac{-1+\sqrt{3}i}{2} $ then $ {{(3+\omega +3{{\omega }^{2}})}^{4}} $ = [Karnataka CET 2004; Pb. CET 2000]
Options:
A) 16
B) -16
C) 16 $ \omega $
D) 16 $ {{\omega }^{2}} $
Show Answer
Answer:
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}} $ .
BETA
