A) 6
B) 5
C) 4
D) 3
Correct Answer: D
Solution :
We have, \[{{(1+{{\omega }^{2}})}^{m}}={{(1+{{\omega }^{4}})}^{m}}\] \[(\because \,\,{{\omega }^{3}}=1)\] \[{{(1+{{\omega }^{2}})}^{m}}={{(1+\omega )}^{m}}\] \[{{(-\omega )}^{m}}={{(-{{\omega }^{2}})}^{m}}\] \[\Rightarrow {{\left( \frac{\omega }{{{\omega }^{2}}} \right)}^{m}}=1\]\[\Rightarrow {{({{\omega }^{2}})}^{m}}=1\]\[={{(\omega )}^{2m}}=({{\omega }^{3}})\]\[\Rightarrow m=\frac{3}{2}\] Hence least positive integral value of m is 3.
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