Before answering Problem, reread the Remarks.Describe the set of points on the unit sphere...

Before answering Problem, reread the Remarks.

Describe the set of points on the unit sphere that correspond to each of the following sets in the complex plane.

(a) the numbers on unit circle |z| = 1

(b) the numbers within the open disk |z| < 1

(c) the numbers that are exterior to unit circle, that is, |z| > 1

Remarks COMPARISON WITH REAL ANALYSIS

FIGURE 1.5.10 The method of correspondence in (b) is a stereographic projection