Question

find the mapping (1,i,0)->(0,-1,-1) stereographic projection

Answer 1

I have no clue, but I'm just curious, what class is this for?

Answer 2

First you should know what the value of i is.

Answer 3

I may not know the concept at hand, but \(i=\sqrt{-1}\). Is this a complex geometry course?

Answer 4

complex analysis

Answer 5

hmm, I should have learned this then...

Answer 6

no wonder this is on page 7... would you like an example problem from Schaum's?

Answer 7

yes please

Answer 8

part one well, there is no problem in the book(nor do I have notes on it).... weird. But here is the section on it.
Let P [fig] be the complex plane and consider a sphere S tangent to P at z=0. The diameter NS is perpendicular to P and we call points N and S the north and south poles of S. Corresponding to any point A on P we can construct line NA intersecting S at point A'.

Answer 9

part 2
Thus to each point of the complex plane P there corresponds one and only one point of the sphere S, and we can represent any complex number by a point on the sphere. For completeness we say that the point N itself corresponds to the "point at infinity" of the plane. The set of all points of the complex plane including the point at infinity is called the entire complex plane, the entire z plane, or the extended complex plane.

Answer 10

The above method for mapping the plane on to the sphere is called stereographic projection. The sphere is sometimes called the Riemann sphere. When the diameter of the Riemann sphere is chosen to be unity, the equator corresponds to the unit circle of the complex plane.

Answer 11

So, that is the entire section which is never spoken of again...

Answer 12

no problem nor example on the topic... Sorry :(

Answer 13

maybe check out the riemann mapping theorem