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IMC 2013/2/1

Source: Imc 2013 Problem 6

August 9, 2013
inequalitiestrigonometryquadraticsfunctioncomplex analysisIMCcollege contests

Problem Statement

Let z\displaystyle{z} be a complex number with ∣z+1∣>2\displaystyle{\left| {z + 1} \right| > 2}. Prove that ∣z3+1∣>1\displaystyle{\left| {{z^3} + 1} \right| > 1}.
Proposed by Walther Janous and Gerhard Kirchner, Innsbruck.
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