Complex Numbers And Quadratic Equations question 244
Question: If $ \omega $ is a complex cube root of unity, then $ (x-y)(x\omega -y) $ $ (x{{\omega }^{2}}-y)= $
Options:
A) $ x^{2}+y^{2} $
B) $ x^{2}-y^{2} $
C) $ x^{3}-y^{3} $
D) $ x^{3}+y^{3} $
Show Answer
Answer:
Correct Answer: C
Solution:
$ (x-y)(x\omega -y)(x{{\omega }^{2}}-y) $ $ =(x^{2}\omega -xy-xy\omega +y^{2})(x{{\omega }^{2}}-y) $ $ =x^{3}-x^{2}y(1+\omega +{{\omega }^{2}})+xy^{2}(1+\omega +{{\omega }^{2}})-y^{3} $ $ =x^{3}-y^{3} $ $ (\because 1+\omega +{{\omega }^{2}}=0) $
BETA
