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 \((| \alpha | + |\gamma |)^2\) ?
