AP EAMCET · Maths · Complex Number
\(\sum_{n=1}^{20}\left[\sin \left(\frac{2 n \pi}{21}\right)-i \cos \left(\frac{2 n \pi}{21}\right)\right]=\)
- A \(1\)
- B \(-1\)
- C \(i\)
- D \(-i\)
Answer & Solution
Correct Answer
(C) \(i\)
Step-by-step Solution
Detailed explanation
\(\sum_{n=1}^{20}\left[\sin \left(\frac{2 n \pi}{21}\right)-i \cos \left(\frac{2 n \pi}{21}\right)\right] = \sum_{n=1}^{20}\left[-i\left(\cos \left(\frac{2 n \pi}{21}\right)+i \sin \left(\frac{2 n \pi}{21}\right)\right)\right]\)…
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