At 2007 Western China MO was problem like this. Dirichle's method can help for proving this fact: $ X_{1},X_{2},X_{3},n$ - real numbers there exist $ b_{i}\le n,a_{i}$, such that $ |a_{i}-b_{i}X_{i}|<\frac{1}{n}$

Something seems messed up in this problem. There do not exist such complex numbers. In fact, there do not even exist $a,b\in\mathbb{C}\setminus\{0\}$ satisfying $|ka+lb|>x$ for some positive real constant $x$ whenever $|k|+|l|\ge 1996$. (This is stronger because we forced ourselves to choose $m=0$.) Here, we may assume $b=1$ because we may divide by $|b|$. Now, we just need to show that $|ka+l|$ can be arbitrarily small for arbitrarily large $|k|,|l|$, which follows from Dirichlet's Approximation Theorem.