Show that the stereographic projections of the points z and 1/.z are reflections of each other in the equatorial plane

Question:

(a) Show that the stereographic projections of the points and 1/.are reflections of each other in the equatorial plane of the Riemann sphere.

(b) Show that the stereographic projections of the points and −1/.are diametrically opposite points on the Riemann sphere.

Answer:

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