Solving $\sum_n^\infty x_n^2 + 2 x_n y_n - y_n^2 = 0$

Question

Trying to figure out of what form the isotropic vectors of V are, where $v \in V = (s_1, s_2, ... )$ with $s_n \in \mathbb{C}$ and the bilinear form is $B(v,w) = \sum_n v_n w_n$

Any simple way of determining this?