Problem

Source: Romania National Olympiad 2013,grade 10 -P2

Tags: inequalities, complex numbers, inequalities proposed



To be considered the following complex and distinct a,b,c,d. Prove that the following affirmations are equivalent: i)For every zC the inequality takes place :|za|+|zb||zc|+|zd|; ii)There is t(0,1) so that c=ta+(1t)b si d=(1t)a+tb