Complex Numbers And Quadratic Equations question 280
Question: The value of $ (1-\omega +{{\omega }^{2}}){{(1-{{\omega }^{2}}+\omega )}^{6}} $ , where $ \omega ,{{\omega }^{2}} $ are cube roots of unity [DCE 2001]
Options:
A) 128 $ \omega $
B) $ -128{{\omega }^{2}} $
C) $ -128\omega $
D) $ 128{{\omega }^{2}} $
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Answer:
Correct Answer: C
Solution:
$ (1-\omega +{{\omega }^{2}}){{(1-{{\omega }^{2}}+\omega )}^{6}} $ $ =(-2\omega ){{(-2{{\omega }^{2}})}^{6}}=-128\omega . $
BETA
