A) \[1\]
B) \[\omega \]
C) \[{{\omega }^{2}}\]
D) \[-1\]
E) 0
Correct Answer: E
Solution :
\[\frac{a+b\omega +c{{\omega }^{2}}}{c+a\omega +b{{\omega }^{2}}}+\frac{c+a\omega +b{{\omega }^{2}}}{a+b\omega +c{{\omega }^{2}}}+\frac{b+c\omega +a{{\omega }^{2}}}{b+c{{\omega }^{4}}+a{{\omega }^{5}}}\] \[=\frac{{{\omega }^{2}}(a+b\omega +c{{\omega }^{2}})}{(a+b\omega +c{{\omega }^{2}})}+\frac{\omega (a\omega +b{{\omega }^{2}}+c)}{(a\omega +b{{\omega }^{2}}+c)}\] \[+\frac{b+c\omega +a{{\omega }^{2}}}{b+c\omega +a{{\omega }^{2}}}\] \[={{\omega }^{2}}+\omega +1=0\]
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