Complex Numbers And Quadratic Equations question 288
Question: If $ \omega $ is a non real cube root of unity, then $ (a+b) $ $ (a+b\omega ) $ $ (a+b{{\omega }^{2}}) $ is [Kerala (Engg.) 2002]
Options:
A) $ a^{3}+b^{3} $
B) $ a^{3}-b^{3} $
C) $ a^{2}+b^{2} $
D) $ a^{2}-b^{2} $
Show Answer
Answer:
Correct Answer: A
Solution:
$ (a+b)(a+b\omega )(a+b{{\omega }^{2}}) $ $ =(a+b)(a^{2}+ab(\omega +{{\omega }^{2}})+b^{2}{{\omega }^{3}}) $ $ =(a+b)(a^{2}-ab+b^{2})=a^{3}+b^{3} $ .
BETA
