extended complex plane

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The set of complex numbers with a point at infinity. The set can be denoted by C∞ and can be thought of as a Riemann sphere by means of a stereographic projection. If a sphere is placed so that a point S on the sphere is touching the complex plane at the origin, then S corresponds to the point (0,0) on the complex plane, which is the complex number z=0. All other points on the sphere, except N which is diametrically opposite to S on the sphere, are in a one-to-one correspondence with points on the complex plane through the stereographic projection, and therefore with a unique complex number. The point N is identified with the point at infinity, with corresponding complex number ∞.

Subjects: Mathematics.

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