WBJEE · Maths · Complex Number
If \(Z_{r}=\sin \frac{2 \pi}{11}-i \cos \frac{2 \pi}{11},\) then \(\sum_{r=0}^{10} Z_{r}\) is equal to
- A -1
- B 0
- C i
- D \(-i\)
Answer & Solution
Correct Answer
(B) 0
Step-by-step Solution
Detailed explanation
We have, \(Z,=\sin \frac{2 \pi r}{11}-i \cos \frac{2 \pi}{11}\) \[ =-i\left(\cos \frac{2 \pi r}{11}+i \sin \frac{2 \pi r}{11}\right) \] \(\therefore\)…
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