Koiran's real -conjecture asserts that if a non-zero real polynomial can be written as f=pi=1qj=1fij , where each fij contains at most k monomials, then the number of distinct real roots of f is polynomial in pqk. We show that the conjecture implies quite a strong property of the complex roots of f: their arguments are uniformly distributed except for an error which is polynomial in pqk. That is, if the conjecture is true, f has degree n and f(0)=0 , then for every 00 and , counted with multiplicities. In particular, if the real -conjecture is true, it is also true when multiplicities of non-zero real roots are included.