text: does anyone know, what are hypercomplex numbers?   hypercomplex numbers, better known as quaternions, were discovered by hamilton in the nineteenth century. it had long been appreciated that the real numbers have a geometrical interpretation as points lying on a line, and that the complex numbers have a similar geometrical interpretation as points lying in a plane. as hamilton pointed out in a paper in 1833, the addition symbol used in the cartesian representation of a complex number   a+ib,  is somewhat misleading, since a real and purely imaginary number cannot be directly added together arithmetically.  a more suitable representation might be as an ordered pair of real numbers   (a,b),  together with a set of manipulation rules that define how to perform operations like addition and multiplication of these pairs.