JEE Mains · Maths · STD 11 - 4.1 complex nubers
Let \(\mathrm{z}=\frac{1-i \sqrt{3}}{2}, i=\sqrt{-1} .\) Then the value of \(21+\left(z+\frac{1}{z}\right)^{3}+\left(z^{2}+\frac{1}{z^{2}}\right)^{3}+\left(z^{3}+\frac{1}{z^{3}}\right)^{3}+\ldots+\left(z^{21}+\frac{1}{z^{21}}\right)^{3}\) is .... .
- A \(12\)
- B \(11\)
- C \(19\)
- D \(13\)
Answer & Solution
Correct Answer
(D) \(13\)
Step-by-step Solution
Detailed explanation
\(Z=\frac{1-\sqrt{3} i}{2}=e^{-i \frac{\pi}{3}}\) \(z^{r}+\frac{1}{z^{r}}=2 \cos \left(-\frac{\pi}{3}\right) r=2 \cos \frac{\mathrm{r} \pi}{3}\)…
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