AP EAMCET · Maths · Complex Number
\(\sum_{k=1}^6 \sin \left(\frac{2 \pi k}{7}\right)-i \cos \left(\frac{2 \pi k}{7}\right)=\)
- A \(1\)
- B \(-i\)
- C \(i\)
- D \(-1\)
Answer & Solution
Correct Answer
(C) \(i\)
Step-by-step Solution
Detailed explanation
\(\sum_{k=1}^6-i\left[\cos \frac{2 \pi k}{7}+i \sin \frac{2 \pi k}{7}\right]\) \(\cos \theta+i \sin \theta=e^{i \theta}\) \((-i) \sum_{k=1}^6 e^{i \frac{2 \pi k}{7}}\)…
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