Abstract: The study of complex points was initiated in 1965 by E. Bishop with his seminal work on real smooth submanifolds in complex Euclidean spaces; a point $p\in M$ of a real smooth $2n$-submanifold $M\subset \mathbb{C}^{n+1}$ is called complex when $T_pM$ is a complex subspace in $T_p\mathbb{C}^{n+1}$.

In this talk we consider the behavior of the quadratic part of complex points of small $\mathcal{C}^2$ -perturbations of real 4-manifolds embedded in a complex 3-manifold. More precisely, we describe the change of the structure of the quadratic normal form of a complex point. It is an immediate consequence of a theorem clarifying how small perturbations can change the bundle of a pair of one arbitrary and one symmetric $2 \times 2$ matrix with respect to an action of a certain linear group. This is a continuation of our previous work on the quadratic part of complex points.