A) \[\frac{1-i\sqrt{3}}{2}\]
B) \[-\frac{1-i\sqrt{3}}{2}\]
C) 1
D) (b) and (c) both
Correct Answer: D
Solution :
The product is given by \[\omega .{{\omega }^{2}}.{{\omega }^{3}}.....{{\omega }^{n}}={{\omega }^{1+2+3+......+n}}={{\omega }^{n(n+1)/2}}\] On putting \[n=1,2,3,.....,\]we get \[={{\omega }^{1(1+1)/2}}=\omega ,{{\omega }^{2(2+1)/2}}={{\omega }^{3}}=1,.....{{\omega }^{4(5)/2}}={{\omega }^{10}}=\omega \] Hence it gives the values 1 and \[\omega \] only.You need to login to perform this action.
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