Hypercomplex numbers

Hypercomplex numbers extend the familiar concept of complex numbers (which combine real and imaginary parts) into higher dimensions. Unlike regular complex numbers (two parts), hypercomplex systems can have three, four, or more components, enabling the representation of more complex phenomena like rotations and symmetries in advanced mathematics and physics. Examples include quaternions (4 components) used for 3D rotations and octonions (8 components). They retain algebraic properties similar to complex numbers but operate in higher-dimensional spaces, providing powerful tools for modeling problems in computer graphics, quantum physics, and engineering.