To be considered the following complex and distinct a,b,c,d. Prove that the following affirmations are equivalent: i)For every z∈C the inequality takes place :|z−a|+|z−b|≥|z−c|+|z−d|; ii)There is t∈(0,1) so that c=ta+(1−t)b si d=(1−t)a+tb
Problem
Source: Romania National Olympiad 2013,grade 10 -P2
Tags: inequalities, complex numbers, inequalities proposed