Complex Numbers And Quadratic Equations question 276
Question: If $ \omega $ is an imaginary cube root of unity, $ {{(1+\omega -{{\omega }^{2}})}^{7}} $ equals [IIT 1998; MP PET 2000]
Options:
A) $ 128\omega $
B) $ -128\omega $
C) $ 128{{\omega }^{2}} $
D) $ -128{{\omega }^{2}} $
Show Answer
Answer:
Correct Answer: D
Solution:
$ {{(1+\omega -w^{2})}^{7}}={{(1+\omega +{{\omega }^{2}}-2{{\omega }^{2}})}^{7}}={{(-2{{\omega }^{2}})}^{7}} $ $ =-128{{\omega }^{14}}=-128{{\omega }^{12}}{{\omega }^{2}}=-128{{\omega }^{2}} $
BETA
