Problem

Source: Iran MO Third Round 2021 A2

Tags: algebra



If $a, b, c$ and $d$ are complex non-zero numbers such that $$2|a-b|\leq |b|, 2|b-c|\leq |c|, 2|c-d| \leq |d| , 2|d-a|\leq |a|.$$Prove that $$\frac{7}{2} <\left| \frac{b}{a} + \frac{c}{b} + \frac{d}{c} + \frac{a}{d} \right| .$$