Thanks.

(5) In this problem you work out a few details about the Riemann sphere S, which we will take as the sphere I? | I; + I: = 1: where the centre is the origin of the complex planeI and we label points in that plane as .3 = I + iy as usual. We associate each point of 3 except its north pole (0,0,1)I with the point 31 +1352 2: = . 1 1'3 The point (0,0,1)I is associated to oo. {a} Find |z|2 in terms of 2:3. {b} Find $3,552,533 in terms of 3,3. {c} [optionaljI Show that 1." 0 y 0 2: 1 931 to _ 1'3 1 and hence that the points (my, 0), ($1,532,:E3), (0,0, 1) are collinear. This is the atereographic projection mentioned in your book