How do I know that $$e^{\pi i /15}$$ is algebraic number? I know it is from the worlfram, but I don't know what method I can use to find if a number is algebraic.
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4It's a root of $x^{15}+1$. – B. Goddard Mar 11 '20 at 16:31
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It solves $z^{15}=-1$ – J. W. Tanner Mar 11 '20 at 16:31
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Hint: Raise it to the power 15. – Gary Mar 11 '20 at 16:31
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Starting from knowing that $e^{i\pi} = -1$, it is possible to factor $i \pi$ as $15\frac{i \pi} {15}$, hence we have $$ (e^{\frac{i \pi}{15}})^{15} = -1$$
Therefore it is possible to obtain this number by solving the polynomial $ z^{15} + 1 = 0 $.
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