Riemann Sphere

The Riemann Sphere is a way mathematicians visualize all complex numbers, including infinity, arranged on a sphere. Imagine taking the entire complex plane (numbers with real and imaginary parts) and "wrapping" it onto a sphere so that each point corresponds to a unique number. The point at infinity is represented as the "north pole" of the sphere. This model allows for smooth, continuous treatment of complex functions, even at infinity, and provides a powerful tool to understand complex analysis and the behavior of functions across all points—including those that tend toward infinity.