Before answering Problem, reread the Remarks. Express the coordinates of the point (x0, y0...

Before answering Problem, reread the Remarks. Express the coordinates of the point (x0, y0, u0) on the unit sphere in Figure in terms of the coordinates of the point (a, b, 0) in the complex plane. Use these formulas to verify your answer to Problem. [Hint: First show that all points on the line containing (0, 0, 1) and (a, b, 0) are of the form (ta, tb, 1 − t).]

Problem

Find a point (x0, y0, u0) on the unit sphere that corresponds to the complex number 2 + 5i. See Figure.

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

Remarks COMPARISON WITH REAL ANALYSIS

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