An extremal problem for polynomials

We give a solution to an extremal problem for polynomials, which asks for complex numbers α₀,…,α_n${\alpha }_0,\dots ,{\alpha }_n$ of unit magnitude that minimise the largest supremum norm on the unit circle for all polynomials of degree n whose k  -th coefficient is either α_k${\alpha }_k$ or −α_k$-{\alpha }_k$.