Question 38
Let $n$ be a positive integer and $A$ be a set of complex numbers with $2n + 1$ elements. Prove that there exists two sets $B, C$ so that $B \cup C = A$, $B \cap C = \emptyset$, $B$ has $n$ elements and $|\sum_{z \in B} z| \le |\sum_{z \in C} z|$.