MCQOPTIONS
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MCQOPTIONS
| 1. |
If \[{{z}_{r}}=\cos \frac{r\alpha }{{{n}^{2}}}+i\sin \frac{r\alpha }{{{n}^{2}}},\] where r = 1, 2, 3,?.,n, then \[\underset{n\to \infty }{\mathop{\lim }}\,\,\,{{z}_{1}}{{z}_{2}}{{z}_{3}}...{{z}_{n}}\] is equal to [UPSEAT 2001] |
| 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. \[\sqrt[3]{{{e}^{i\alpha }}}\] | |