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The extended complex plane

  1. Feb 16, 2014 #1
    In a report I am writing I want to define the extended complex plane/Riemann Sphere and I would like to check if I grasp the concept properly:
    Consider the Euclidean space [itex]\mathbb{R}^3[/itex] where the [itex]x-y[/itex] plane represents [itex]\mathbb{C}[/itex]. Consider the sphere with south pole [itex](0,0,0)[/itex] and north pole [itex](0,0,\infty)[/itex]. For any point in the [itex]x-y[/itex] plane there exists a unique point where the straight line from this point to the north pole crosses the sphere. Hence the complex plane [itex]\mathbb{C}[/itex] can be mapped bijectively onto this sphere.

    I know this isn't rigorous but as a worded explanation of the concept does this capture the crux of the matter.

    Jim
     
  2. jcsd
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