# Sylvester Gallai theorem in the complex space

An extension of Sylvester-Gallai theorem to the complex space $\mathbb{C}^d$ by Kelly states that if every line passes through at least 3 points in the given set, then these points have to be coplanar. My question, what is coplanarity in complex space ? Does it mean the dimension of the affine space containing these points is $\leq$ 4?