Question 26
Let $a$, $b$, $c$, $d$ be four non-zero complex numbers such that
$$
2|a - b| \le |b|, \quad 2|b - c| \le |c|, \quad 2|c - d| \le |d|, \quad 2|d - a| \le |a|.
$$
Prove that
$$
\left| \frac{b}{a} + \frac{c}{b} + \frac{d}{c} + \frac{a}{d} \right| \gt \frac{7}{2}.
$$
$$
2|a - b| \le |b|, \quad 2|b - c| \le |c|, \quad 2|c - d| \le |d|, \quad 2|d - a| \le |a|.
$$
Prove that
$$
\left| \frac{b}{a} + \frac{c}{b} + \frac{d}{c} + \frac{a}{d} \right| \gt \frac{7}{2}.
$$