Real and complex planes and hyperplanes. (Planos e hiperplanos reais e complexos.) (Portuguese)

Bol. Soc. Parana. Mat. (3) 21, No. 1-2, 137-143 (2003).

The study of the structure of n-dimensional complex space $C^n$ and the different objects in this space is very important, both for analysis of properties of $C^n$ and for investigations of functions of n complex variables. In this article, real and complex planes and hyperplanes in the space $C^n$ are considered. In particular, equations for complex line and real two-dimensional plane are constructed. The following statement is proved: any two distinct complex lines can have at most one common point in the space $C^n$ (n $\ge$ 2). One example shows that a similar statement is not true for two distinct real two-dimensional planes in $C^n$.