[JEE Advanced 1987] The value of $\sum_{k=1}^{6}\left(\sin\frac{2\pi k}7-i\cos\frac{2\pi k}7\right)$ is
The value of $\sum_{k=1}^{6}\left(\sin\frac{2\pi k}7-i\cos\frac{2\pi k}7\right)$ is
(a) $-1$
(b) $0$
(c) $-i$
(d) $i$
1 Answer
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✓ Vidaara Team
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· 1mo ago
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Correct answer: (d) $i$
$=-i\sum_{k=1}^{6}e^{i2\pi k/7}=-i(0-1)=i$ (the full sum of 7th roots is $0$).
JEE Advanced 1987 · Complex Numbers — verified solution by the Vidaara Team.
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