Is it possible to analytically find the roots of the polynomial $\mathbf{1 + s^{12}}$ where $s$ denotes the Laplace variable? I know that the roots will appear in complex-conjugate pairs lying on the unit circle in the $s$-plane.
2026-03-29 04:41:25.1774759285
How to find the Roots of the Polynomial $1 + s^{12}$ analytically
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Hint: $1+s^{12}=0$ iff $s^{12}=-1$ iff $s^{24}=1$ and $s^{12}\ne1$.