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Q: Where does z = 2 (real) project on the Riemann sphere? What about z → ∞? Stereographic: line from north pole N through z hits sphere. z = 2: projects to southern hemisphere point (below equator, since |z|>1!). |z| = 1: equator! |z| < 1: northern hemisphere! z → ∞: approaches NORTH POLE - ∞ is a point (one-point compactification!)!