JEE Mains · Maths · STD 11 - 4.1 complex nubers
Let \(\alpha=\frac{-1+i\sqrt{3}}{2}\) and \(\beta=\frac{-1-i\sqrt{3}}{2}\),\(i=\sqrt{-1}\). If \((7-7\alpha+9\beta)^{20}+(9+7\alpha-7\beta)^{20}+(-7+9\alpha+7\beta)^{20}+(14+7\alpha+7\beta)^{20}=m^{10}\) then m is ___ .
- A 7
- B 14
- C 21
- D 49
Answer & Solution
Correct Answer
(D) 49
Step-by-step Solution
Detailed explanation
\(\left(9+7 \omega-7 \omega^2\right)+\omega^{20}\left(9+7 \omega-7 \omega^2\right)^{20}+\) \(\omega^{40}\left(9+7 \omega-7 \omega^2\right)^{20}+\left(14+7\left(\omega+\omega^2\right)\right)^{20}\)…
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