Complex Numbers And Quadratic Equations question 273
Question: If $ \omega $ is the cube root of unity, then $ {{(3+5\omega +3{{\omega }^{2}})}^{2}} $ + $ {{(3+3\omega +5{{\omega }^{2}})}^{2}} $ = [MP PET 1999]
Options:
A) 4
B) 0
C) - 4
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ {{(3+5\omega +3{{\omega }^{2}})}^{2}}+{{(3+3\omega +5{{\omega }^{2}})}^{2}} $ $ ={{(3+3\omega +3{{\omega }^{2}}+2\omega )}^{2}}+{{(3+3\omega +3{{\omega }^{2}}+2{{\omega }^{2}})}^{2}} $ $ (1+\omega +{{\omega }^{2}}=0,{{\omega }^{3}}=1) $ $ ={{(2\omega )}^{2}}+{{(2{{\omega }^{2}})}^{2}}=4{{\omega }^{2}}+4{{\omega }^{4}}=4(-1)=-4 $ .
BETA
