Complex Numbers And Quadratic Equations question 294
Question: If $ 1,\omega ,{{\omega }^{2}} $ are the roots of unity, then $ {{(1-2\omega +{{\omega }^{2}})}^{6}} $ is equal to [Pb. CET 2001]
Options:
A) 729
B) 246
C) 243
D) 81
Show Answer
Answer:
Correct Answer: A
Solution:
$ {{(1-2\omega +{{\omega }^{2}})}^{6}} $ = $ {{(1+{{\omega }^{2}}-2\omega )}^{6}} $ = $ {{(-\omega -2\omega )}^{6}}={{(-3\omega )}^{6}} $ $ ={{(-3)}^{6}}{{({{\omega }^{3}})}^{2}} $ [Since $ 1+\omega +{{\omega }^{2}}=0,{{\omega }^{3}}=1 $ ] = 729.
BETA
