[JEE Main 2006] the value of sum k 1 10 sin 2k pi 11 i cos 2k
The value of $\sum_{k=1}^{10}\left(\sin\frac{2k\pi}{11}+i\cos\frac{2k\pi}{11}\right)$ is
(a) $i$
(b) $1$
(c) $-1$
(d) $-i$
1 Answer
VAVidaara Admin
✓ Vidaara Team
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· 2d ago
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Correct answer: (d) $-i$
$=i\sum_{k=1}^{10}e^{-i2k\pi/11}=i(0-1)=-i$ (the full sum of 11th roots is $0$).
JEE Main 2006 · Complex Numbers — verified solution by the Vidaara Team.
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