Complex Numbers And Quadratic Equations question 239
Question: If $ \omega $ is a cube root of unity, then $ {{(1+\omega )}^{3}}-{{(1+{{\omega }^{2}})}^{3}}= $
Options:
A) 0
B) $ \omega $
C) $ {{\omega }^{2}} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ {{(1+\omega )}^{3}}-{{(1+{{\omega }^{2}})}^{3}}={{(-{{\omega }^{2}})}^{3}}-{{(-\omega )}^{3}} $ $ =-{{\omega }^{6}}+{{\omega }^{3}}=-{{\omega }^{3}}{{\omega }^{3}}+{{\omega }^{3}}=-1+1=0 $
BETA
