AP EAMCET · Maths · Complex Number
If \(\rho\) is a complex cube root of unity, then
\(\cos \left(\sum_{k=1}^7(k-\omega)\left(k-\omega^2\right) \frac{\pi}{175}\right)=\)
- A \(-1\)
- B 0
- C 1
- D 5
Answer & Solution
Correct Answer
(A) \(-1\)
Step-by-step Solution
Detailed explanation
We have to calculate \(\cos \left(\sum_{k=1}^7(k-\omega)\left(k-\omega^2\right) \frac{\pi}{175}\right)\) \(=\cos \left(\sum_{k=1}^7\left(k^2-k \omega^2-k \omega+\omega^3\right) \frac{\pi}{175}\right)\) \(=\cos \left(\sum_{k=1}^7\left(k^2-k x(-1)+1\right) \frac{\pi}{175}\right)\)…
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