Stereographic projection on complex plane

Reference no: EM13127667

Let V be a circle lying in S. Then there is a unique plane P in R^3 such that p / S = V ( / = intersection). Recall from analytuc geomerty that

P = { (x_1,x_2,x_3) : x_1 b_1 + x_2 b_2 + x_3 b_3 = L, where L is a real number}.

Where ( b_1,b_2,b_3) is a vector orthogonal to P . It can be assumed that (b_1)^2 + (b_2)^2 + (b_3)^2=1. Use this information to show that if V contains the point N then its seteographic projection on the complex plane is a straight line. Otherwise, V projects onto a circle in complex plane.

N = (0,0,1) the north pole on S

Please explain to me every step, I don't just want the answer, but I also want to understand it and be able to work similar problems.

Reference no: EM13127667

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