  In this article, we investigate the quantitative unique continuation
properties of complex-valued solutions to drift equations in the plane. We
consider equations of the form $\Delta u + W \cdot \nabla u = 0$ in
$\mathbb{R}^2$, where $W = W_1 + i W_2$ with each $W_j$ real-valued. Under the
assumptions that $W_j \in L^{q_j}$ for some $q_1 \in [2, \infty]$, $q_2 \in (2,
\infty]$, and $W_2$ exhibits rapid decay at infinity, we prove new global
unique continuation estimates. This improvement is accomplished by reducing our
equations to vector-valued Beltrami systems. Our results rely on a novel order
of vanishing estimate combined with a finite iteration scheme.
