Complex Numbers And Quadratic Equations question 291
Question: If $ \omega $ is a complex cube root of unity, then $ 225+ $ $ {{(3\omega +8{{\omega }^{2}})}^{2}} $ $ +{{(3{{\omega }^{2}}+8\omega )}^{2}}= $ [EAMCET 2003]
Options:
A) 72
B) 192
C) 200
D) 248
Show Answer
Answer:
Correct Answer: D
Solution:
$ 225+{{(3\omega +8{{\omega }^{2}})}^{2}}+{{(3{{\omega }^{2}}+8\omega )}^{2}} $ $ =225+{{(5{{\omega }^{2}}-3)}^{2}}+{{(5\omega -3)}^{2}} $ $ =225+18-5(\omega +{{\omega }^{2}}) $ $ =225+18-5(-1)=225+18+5=248. $
BETA
