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Let us consider the following set of $ \mathbb{C}^2$ : $ $ N=\{(|a|^2-4|b|^2,4a\overline{b}+b\overline{a});\;(a,b) \in \mathbb{C}^2\;\;\hbox{and}\;|a|^2+4|b|^2=1\} $ $ I want to prove that $ N$ is a convex set of $ \mathbb{C}^2$ . Thank youRead more