What is the relation satisfied by two ponts z1,z2 which are the images under stereographic projection of a pair of diametrically opposite points of the Riemann sphere?

Question

anonymous · Answer

maybe this would be a start:
diametrically opposite means that the points belong to opsite emispheres North-South, esat-west. That means that one of the z is mapped inside circle, the other outside. And one would be in upper part of the plane and the other down part...

experimentx · Answer

looks like some crazy stuff ... lol

anonymous · Answer

complex analysis...

experimentx · Answer

though i would also like to gain some insight.

anonymous · Answer

actually i have a guess, but not sure about it..

anonymous · Answer

i would say z*conjugate(z) = -1

anonymous · Answer

just lloks like when changing from spherical coordinates on the sphere to cartesian on the complex plain...

experimentx · Answer

I never read those stuff ... since i was physics major. though it seems interesting.

anonymous · Answer

most probably its : $$(z)*conjugate (z) = 1$$

anonymous · Answer

how you got that @Aron_West, can you show steps?

anonymous · Answer

i still insist on z*conjugate(z) = -1

experimentx · Answer

what you are searching for might be here ... sometimes google is qutie smart http://adsabs.harvard.edu/full/1984QJRAS..25..126S https://www.google.com/search?rlz=1C1ASUT_enNP447NP447&sourceid=chrome&ie=UTF-8&q=z1%2Cz2+which+are+the+images+under+stereographic+projection+of+a+pair+of+diametrically+opposite+points+of+the+Riemann+sphere%3F

anonymous · Answer

thx