Erdős problem 498

Let $z_1,\ldots,z_n\in\mathbb{C}$ with $1\leq \lvert z_i\rvert$ for $1\leq i\leq n$. Let $D$ be an arbitrary disc of radius $1$. Is it true that the number of sums of the shape $$\sum_{i=1}^n\epsilon_iz_i \textrm{ for }\epsilon_i\in \{-1,1\}$$ which lie in $D$ is at most $\binom{n}{\lfloor n/2\rfloor}$?