Let

be a fixed complex number. In this paper, we study the quantity

, where

is the set of all real polynomials of degree at most n-1 with coefficients in the interval [0, 1]. We first show how, in principle, for any given

and

, the quantity S(

, n) can be calculated. Then we compute the limit

for every

of modulus 1. It is equal to 1/

if

is not a root of unity. If

, where

and k

[1, d-1] is an integer satisfying gcd(k, d) = 1, then the answer depends on the parity of d. More precisely, the limit is 1, 1/(d sin(

/d)) and 1/(2d sin(

/2d)) for d = 1, d even and d > 1 odd, respectively.