Complex Numbers And Quadratic Equations question 242
Question: If $ \omega $ is a cube root of unity, then the value of $ {{(1-\omega +{{\omega }^{2}})}^{5}}+{{(1+\omega -{{\omega }^{2}})}^{5}}= $ [IIT 1965; MP PET 1997; RPET 1997]
Options:
A) 16
B) 32
C) 48
D) - 32
Show Answer
Answer:
Correct Answer: B
Solution:
$ {{(1-\omega +{{\omega }^{2}})}^{5}}+{{(1+\omega -{{\omega }^{2}})}^{5}} $ $ ={{(-2\omega )}^{5}}+{{(-2{{\omega }^{2}})}^{5}}=-32{{\omega }^{3}}{{\omega }^{2}}-32{{({{\omega }^{3}})}^{3}}\omega $ $ =-32({{\omega }^{2}}+\omega )=-32(-1)=32 $
BETA
