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.
2026-02-23 06:34:51.1771828491
algebraic number $e^{\pi i /15}$
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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 $.