Represent a DNF formula as a multivariate linear formula?
Usually one represents disjunction by addition and conjunction by multiplication, so a suitable polynomial would be $(x + y) \cdot (z + w)$ (I renamed $i$ to $w$ here as to not create confusion w.r.t. the imaginary unit).
Note that plugging in $0$ or $1$ depending on the desired truth values yields 0 precisely if the original formula would evaluate to false while any value greater than zero indicates that such an assignment would satisfy the formula.
You mention linear in your title, however I do not think that there is a sensible way to represent propositional formulas by linear functions.