A) - 1
B) 0
C) 9
D) i
Correct Answer: A
Solution :
\[\omega +{{\omega }^{\left( \frac{1}{2}+\frac{3}{8}+\frac{9}{32}+\frac{27}{128}+..... \right)}}\] \[=\frac{(1-\cos \theta )-i\sin \theta }{{{(1-\cos \theta )}^{2}}+{{\sin }^{2}}\theta }\] \[\omega +{{\omega }^{\left( \frac{1/2}{1-3/4} \right)}}\] \[\Rightarrow \] \[\omega +{{\omega }^{2}}=-1\] \[[\because 1+\omega +{{\omega }^{2}}=0]\]
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