Complex Numbers And Quadratic Equations question 241
Question: If w is a complex cube root of unity, then $ (1-\omega )(1-{{\omega }^{2}}) $ $ (1-{{\omega }^{4}})(1-{{\omega }^{8}})= $
Options:
A) 0
B) 1
C) - 1
D) 9
Show Answer
Answer:
Correct Answer: D
Solution:
$ (1-\omega )(1-{{\omega }^{2}})(1-{{\omega }^{4}})(1-{{\omega }^{8}}) $ $ =(1-\omega )(1-{{\omega }^{2}})(1-\omega )(1-{{\omega }^{2}})={{(1-\omega )}^{2}}{{(1-{{\omega }^{2}})}^{2}} $ = $ (-3\omega )(-3{{\omega }^{2}})=9{{\omega }^{3}}=9 $ .
BETA
