Must imaginary roots come in conjugate pairs?

The book's answer is nonsense. Your calculation gives a polynomial with roots at $0,\,4,\,i$ as desired and is a very direct way to find the minimal polynomial that will have a root at all of those places. More simply, one can see this phenomenon since $x-i=0$ is a polynomial with a single root at $i$. Complex roots only necessarily come in conjugate pairs for polynomials with real coefficients. As you note, the book's answer would be correct if you were asked to find a real polynomial with those roots.

(Not to mention that this question is terribly ambiguous, since it doesn't seem clear whether the polynomial should have only those three roots, or those three should be among the roots, in which case both (b) and (c) would work)