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.

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.