Let $X$ be a non-solvable $C^{\infty}$ complex vector field in $\Bbb R^2$ satisfying certain conditions. A necessary condition for the equation $Xu=0$ to have a solution $u$ such that $du\ne 0$ near the origin and one for the $Xu=0$ to admit a solution $u$ such that $du\not\equiv 0$ in any sufficiently small neighborhood of the origin\ are given. These are expressed by making use of an estimate.