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Inequality

Source: Romania District Olympiad 2013,grade X(problem 2)

March 14, 2013
inequalitiestrigonometryfunctioninequalities proposed

Problem Statement

Let a,b∈Ca,b\in \mathbb{C}. Prove that ∣az+bzˉ∣≤1\left| az+b\bar{z} \right|\le 1, for every z∈Cz\in \mathbb{C}, with ∣z∣=1\left| z \right|=1, if and only if ∣a∣+∣b∣≤1\left| a \right|+\left| b \right|\le 1.
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