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| ?
Answer Choices
A. 1
B. \sqrt{2}
C. 2
D. 2 \sqrt{2}
E. 4