Yeah, that step from 1.1.10 to 1.1.11 is a bit dense. I think the key is treating the stereographic projection and the complex structure together — maybe try expressing the components explicitly in terms of y1,y2,z1,z2y_1, y_2, z_1, z_2y1,y2,z1,z2 and see how the cross-product forms. That helped...