Hmm, plotting points on the complex plane is very basic compared with algebraic number theory... but I suppose we all have gaps in knowledge.

The link for Eisenstein integers shows the lattice points in the upper right corner of the page, should grab your attention; full size image

here.

For any complex number a+bi, plot it on the complex plane as (a,b) the same way you would plot (x,y) in R^2 normally. Of course

. Where is the difficulty?

Edit: It's occurred to me that "and are rational" could be referring to the "rational integers". I assume based on previous threads that this is a translation from German, and as such, is possibly clearer in the original German, whereas here it seems closer to a typo.