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1answer
59 views

Polynomials with roots having the same module and linear dependent arguments

Is it possible for a polynomial with integer coefficients to have some of its roots: $$m_1e^{i\theta_1 \pi}, m_2e^{i\theta_2 \pi}, \ldots, m_ke^{i\theta_k \pi}$$ such that there exist nonzero integers ...
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1answer
198 views

Polynomials in irrational powers and their roots

When solving an equation with irrational (or algebraic in the case) powers, are the roots likely to be transcendental or algebraic, or does it vary? As an example, I was trying to figure out if $(x + ...