A function f is defined by f(z) \equal{} (4 \plus{} i) z^2 \plus{} \alpha z \plus{} \gamma for all complex numbers z, where α and γ are complex numbers and i^2 \equal{} \minus{} 1. Suppose that f(1) and f(i) are both real. What is the smallest possible value of | \alpha | \plus{} |\gamma |?
<spanclass=′latex−bold′>(A)</span>1<spanclass=′latex−bold′>(B)</span>2<spanclass=′latex−bold′>(C)</span>2<spanclass=′latex−bold′>(D)</span>22<spanclass=′latex−bold′>(E)</span>4