  We introduce the notion of complex $G_2$ manifold $M_{\mathbb C}$, and
complexification of a $G_2$ manifold $M\subset M_{\mathbb C}$. As an
application we show the following: If $(Y,s)$ is a closed oriented $3$-manifold
with a $Spin^{c}$ structure, and $(Y,s)\subset (M, \varphi)$ is an imbedding as
an associative submanifold of some $G_2$ manifold (such imbedding always
exists), then the isotropic associative deformations of $Y$ in the complexified
$G_2$ manifold $M_{\mathbb C}$ is given by Seiberg-Witten equations.
