Use complex numbers to find the sum \( \sum_{r=0}^{n-1} \cos ^{2}\left(\alpha+\frac{r \pi}{n}\ri...
Use complex numbers to find the sum \( \sum_{r=0}^{n-1} \cos ^{2}\left(\alpha+\frac{r \pi}{n}\right) \) where \( \mathrm{n} \in \mathrm{N} ; \mathrm{n} \geq 2 \).
(a) \( \mathrm{n} / 2 \)
(b) \( \mathrm{n} \)
(c) \( 2 \mathrm{n} \)
(d) \( 2 \mathrm{n}-1 \)
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