If \[{{z}_{r}}=\cos \frac{r\alpha }{{{n}^{2}}}+i\sin \frac{r\alpha }{{{n}^{2}}},\] where \[r=1,2,3,...n,\] then \[\underset{x\to \infty }{\mathop{\lim }}\,{{z}_{1}}{{z}_{2}}{{z}_{3}}...{{z}_{n}}\] is equal to

\[\cos (\alpha /2)-i\,\,sin(\alpha /2)\]

If \[{{z}_{r}}=\cos \frac{r\alpha }{{{n}^{2}}}+i\sin \frac{r\alpha }{{

1.	If \[{{z}_{r}}=\cos \frac{r\alpha }{{{n}^{2}}}+i\sin \frac{r\alpha }{{{n}^{2}}},\] where \[r=1,2,3,...n,\] then \[\underset{x\to \infty }{\mathop{\lim }}\,{{z}_{1}}{{z}_{2}}{{z}_{3}}...{{z}_{n}}\] is equal to
A.	\[\cos \alpha +i\sin \alpha \]
B.	\[\cos (\alpha /2)-i\,\,sin(\alpha /2)\]
C.	\[{{e}^{i\alpha /2}}\]
D.	\[\sqrt[3]{{{e}^{i\alpha }}}\]
Answer» D. \[\sqrt[3]{{{e}^{i\alpha }}}\]

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If \[{{z}_{r}}=\cos \frac{r\alpha }{{{n}^{2}}}+i\sin \frac{r\alpha }{{{n}^{2}}},\] where \[r=1,2,3,...n,\] then \[\underset{x\to \infty }{\mathop{\lim }}\,{{z}_{1}}{{z}_{2}}{{z}_{3}}...{{z}_{n}}\] is equal to

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