The extended complex numbers is the complex numbers $\mathbb{C}$, with the complex infinity $\{\tilde{\infty}\}$ adjoined as an element of the set. There is only one infinity in this set, so if you're on the complex plane, and you set out along any line going out to infinity, all the lines meet at the same infinity.
The best way to visualize the extended complex numbers is through one of its representations, the Riemann sphere. In this representation, one can think of the north and south poles of the sphere as infinity and zero, respectively. I encourage you to look through that article (at least the opening paragraph) for more details.