Finding a solutions for an equation

Are half of the $2^n$-th roots of the unit rationally unbiased? Answer

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Are half of the $2^n$-th roots of the unit rationally unbiased?

The following query was motivated by this MO-problem (which in its rotate was motivated by one other MO-post).

I await that the respond ought to breathe identified to consultants (due to very unostentatious formulation)…

Problem. Let $nge 2$. Is the clique of complicated numbers ${e^{ipi okay/2^n}:0le okay<2^n}$ linearly unbiased over the bailiwick of rationals?

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