I'm trying to learn about the "complex plane" C^2, having two complex dimensions, which is supposedly like R^4, which has four real dimensions. I would assume there is a one-to-one correspondance between points in C^2 and the points in R^4. My question at this point is about comparing the "complex lines", C^1, in C^2, and the "real planes", R^2, in R^4. Is there a one-to-one correspondance between the C^1's in C^2 and R^2's in R^4? Or are there more planes in R^4 than "complex lines" in C^2?