If \[\pi /3\] is a complex root of the equation \[{{z}^{3}}=1\], then \[\omega +{{\omega }^{\left( \frac{1}{2}\,+\,\frac{3}{8}\,+\,\frac{9}{32}\,+\,\frac{27}{128}\,+... \right)}}\] is equal to [Roorkee 2000; AMU 2005]

If \[\pi /3\] is a complex root of the equation \[{{z}^{3}}=1\], then

1.	If \[\pi /3\] is a complex root of the equation \[{{z}^{3}}=1\], then \[\omega +{{\omega }^{\left( \frac{1}{2}\,+\,\frac{3}{8}\,+\,\frac{9}{32}\,+\,\frac{27}{128}\,+... \right)}}\] is equal to [Roorkee 2000; AMU 2005]
A.	-1
B.	0
C.	9
D.	i
Answer» B. 0

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If \[\pi /3\] is a complex root of the equation \[{{z}^{3}}=1\], then \[\omega +{{\omega }^{\left( \frac{1}{2}\,+\,\frac{3}{8}\,+\,\frac{9}{32}\,+\,\frac{27}{128}\,+... \right)}}\] is equal to [Roorkee 2000; AMU 2005]

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