AP EAMCET · Maths · Complex Number
\(\sum_{k=1}^6\left(\sin \frac{2 \pi k}{7}-i \cos \frac{2 \pi k}{7}\right)=\)
- A -1
- B 0
- C \(i\)
- D \(-i\)
Answer & Solution
Correct Answer
(C) \(i\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \sum_{k=1}^6\left(\sin \frac{2 \pi k}{7}-i \cos \frac{2 \pi k}{7}\right) \\ & =-i \sum_{k=1}^6\left[\cos \left(\frac{2 \pi k}{7}\right)-\frac{1}{i} \sin \left(\frac{2 \pi k}{7}\right)\right] \\ & =-i \sum_{k=1}^6\left[\cos \left(\frac{2 \pi k}{7}\right)+i \sin…
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