Complex Numbers And Quadratic Equations question 235
Question: If $ \omega $ is a cube root of unity, then $ (1+\omega -{{\omega }^{2}}) $ $ (1-\omega +{{\omega }^{2}}) $ = [MNR 1990; MP PET 1993, 2002]
Options:
A) 1
B) 0
C) 2
D) 4
Show Answer
Answer:
Correct Answer: D
Solution:
If $ \omega $ is a complex cube root of unity then $ {{\omega }^{3}}=1 $ and $ 1+\omega +{{\omega }^{2}}=0 $ , therefore $ (1+\omega -{{\omega }^{2}})(1-\omega +{{\omega }^{2}}) $ $ =(-2{{\omega }^{2}})(-2\omega )=4 $
BETA
