A problem by Δημήτριος Χαλάτσης

Level pending

Suppose three complex numbers \( α_{0},α_{1},α_{2}\) such that

(α-2)(\(\overline{α}\)-2)+|α-2|=2. Also suppose the complex number u such that \(u^{3}\)+\(α_{2}u^{2}\)+\(α_{1}u\)+\(α_{0}\)=0 . Find the smallest integer n : |u|<n

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