Complex Numbers And Quadratic Equations question 287
Question: Find the value of $ {{(1+2\omega +{{\omega }^{2}})}^{3n}}-{{(1+\omega +2{{\omega }^{2}})}^{3n}}= $ [UPSEAT 2002]
Options:
A) 0
B) 1
C) $ \omega $
D) $ {{\omega }^{2}} $
Show Answer
Answer:
Correct Answer: A
Solution:
$ {{[(1+\omega +{{\omega }^{2}})+\omega ]}^{3n}}-{{[(1+\omega +{{\omega }^{2}})+{{\omega }^{2}}]}^{3n}} $ $ ={{\omega }^{3n}}-{{({{\omega }^{2}})}^{3n}} $ $ ={{({{\omega }^{3}})}^{n}}-{{({{\omega }^{3}})}^{2n}} $ $ =1^{n}-1^{2n}=0 $ .
BETA
