RP1 & Complex Half Plane: How Does It Fit?

[tut_einstein]

When you extend the projective line RP1 to the complex half plane, with RP1 as the boundary at infinity, is RP1 the line at infinity for the half plane that we technically cannot "see"? I'm confused about how RP1 fits into the picture of the complex half plane when you make this extension.

Thanks!

 

[mathwonk]

huh? i guess i know what you mean. the real line is the x-axis in the complex plane. then the projective complex line is obtained by adding one point at infinity.

if we consider only the real axis plus that one extra point we do get the real projective ,line.

but what's your question?