IMC 2013 · Problem 1

Day 220th IMC · Blagoevgrad, Bulgaria

Statement

Let $z$ be a complex number with $|z + 1| > 2$ . Prove that $|z^3 + 1| > 1$ .

Hidden so you can work on the problem first.

Proposed by Walther Janous and Gerhard Kirchner, Innsbruck.