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cos(π11)−cos(2π11)+cos(3π11)−cos(4π11)+cos(5π11)= ?\cos\left( \frac{\pi}{11}\right) - \cos\left( \frac{2\pi}{11} \right)+ \cos\left( \frac{3\pi}{11}\right) \\ - \cos\left( \frac{4\pi}{11} \right)+ \cos\left( \frac{5\pi}{11} \right)=\ ?cos(11π)−cos(112π)+cos(113π)−cos(114π)+cos(115π)= ?
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Given z2+z+1=0,z^2+z+1=0,z2+z+1=0, find the value of
(z+1z)2+(z2+1z2)2+(z3+1z3)2+⋯+(z21+1z21)2.\left(z+\dfrac{1}{z} \right)^2+\left(z^2+\dfrac{1}{z^2}\right)^2+\left(z^3+\dfrac{1}{z^3} \right)^2+\cdots+\left(z^{21}+\dfrac{1}{z^{21}}\right)^2.(z+z1)2+(z2+z21)2+(z3+z31)2+⋯+(z21+z211)2.
31−2δ11−2δ1+31−2δ21−2δ2+31−2δ31−2δ3 \dfrac{31-2\delta_{1}}{1-2\delta_{1}} +\dfrac{31-2\delta_{2}}{1-2\delta_{2}}+\dfrac{31-2\delta_{3}}{1-2\delta_{3}} 1−2δ131−2δ1+1−2δ231−2δ2+1−2δ331−2δ3
If 1,δ1,δ2,δ31,\delta_{1},\delta_{2},\delta_{3}1,δ1,δ2,δ3 are distinct fourth roots of unity, then evaluate the expression above.
If w=e2πi/5w=e^{2\pi{i}/5}w=e2πi/5, find ∑k=1411+wk+w2k\sum_{k=1}^{4}\frac{1}{1+w^k+w^{2k}}k=1∑41+wk+w2k1
If for z∈C ,z \in \mathbb{C} \space ,z∈C , z+1z=2cos6°.z+\dfrac{1}{z}=2 \cos 6°.z+z1=2cos6°. Then find the value of (z1000+1z1000).\left( z^{1000}+\frac{1}{z^{1000}} \right).(z1000+z10001).
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