There exist infinitely many inequivalent complex structures in $\mathbb{R}^{2n}$ for all $n \geq 2$.
See for instance the paper
K. Diederich, N. Sibony: Strange complex structures on Euclidean space, Journal für die reine und angewandte Mathematik 311-312, page 397-407 (1979)
and the references given therein.