Funny algebra with imaginary numbers

Let $A(x)$ and $B(x)$ be the polynomials $\displaystyle A(x) = \prod_{k = 1}^{2018} (x + i e^{i \frac{2 \pi k}{2019}})$ and $B(x) = x^2 + 1$ .

Then, there exist two unique polynomials $Q(x)$ of degree $2016$ , and $R(x)$ of degree less than $2$ such that $\forall x \in \mathbb{C}$ , $A(x) = Q(x) \cdot B(x) + R(x)$ .

• Enter $2018 \cdot R(i)$ .

Note.- $i = \sqrt{ -1}$