AP EAMCET · Maths · Complex Number
If \(a=\cos \left(\frac{8 \pi}{11}\right)+i \sin \left(\frac{8 \pi}{11}\right)\), then \(\operatorname{Re}\left(a+a^2+a^3+a^4+a^5\right)=\)
- A 0
- B \(-\frac{1}{2}\)
- C \(\frac{1}{2}\)
- D 1
Answer & Solution
Correct Answer
(B) \(-\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\(a=\cos \left(\frac{8 \pi}{11}\right)+i \sin \left(\frac{8 \pi}{11}\right) \Rightarrow a=e^{\frac{i 8 \pi}{11}}\) \(\Rightarrow a\) is 11 th root of unity and all roots are \(1, a, a^2, \ldots, a^{10}\) Now,…
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