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A function f is defined by \(f(z) = (4 + i) z^2 + \alpha z + \gamma\) for all complex numbers z, where \(\alpha\) and \(\gamma\) are complex numbers and i^2=-1. Suppose that f(1) and f(i) are both real. What is the smallest possible value of \((| \alpha | + |\gamma |)^2\) ?

 Oct 22, 2022
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The smallest possible value is 18

 Oct 22, 2022

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