A) an imaginary number
B) a prime number
C) a positive integer
D) a negative integer.
Correct Answer: D
Solution :
Note that \[m=\omega \] (cube root of unity) |
\[{{(1-\omega )}^{2}}\,{{(\omega -{{\omega }^{2}})}^{2}}\,{{(1-{{\omega }^{2}})}^{2}}\] |
\[=(1+{{\omega }^{2}}-2\omega )\,\,({{\omega }^{2}}+{{\omega }^{4}}-2)\,\,(1+{{\omega }^{4}}-2{{\omega }^{2}})\] |
\[=(-\,3\,\omega )\,(-\,3)\,\,(-\,3\,{{\omega }^{2}})=-\,27\] |
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