Consider the sphere S= {(x,y,z)} ∈ R^3 | x² + y²+ z²=1 }. Let N=(0,0,1) be the north pole of the sphere. The inverse stereographic projection map `s is a homomorphism `s:R^2 s →S-N

defined by mapping the point (x,y) ∈ R^2 to the point on S that lies on the line connection (x,y,0) to N in R^3.

i) find the formula for `s. Make sure to fully justify your answer

ii) Show the circles in the plane with center (0,0) are mapped to circles on the sphere