A) 0
B) 1
C) \[\omega \]
D) \[{{\omega }^{2}}\]
Correct Answer: A
Solution :
We have, \[{{(1+{{\omega }^{2}}+2\omega )}^{3n}}-{{(1+\omega +2{{\omega }^{2}})}^{3n}}\] We know that, \[1+\omega +{{\omega }^{2}}=0\,\,and\,\,{{\omega }^{3}}=1\] \[\therefore \] given expression is equal to \[{{(2\omega -\omega )}^{3n}}\,-{{(2{{\omega }^{2}}-{{\omega }^{2}})}^{3n}}\] \[= {{(\omega )}^{3n}}- {{\left( {{\omega }^{2}} \right)}^{3n}} = {{\left( {{\omega }^{3}} \right)}^{n}} - {{\left( {{\omega }^{3}} \right)}^{2n}} =1-1=0\]
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