Unified View on Complex Numbers and Quaternions
In The 14th IFToMM World Congress, 25.10.-30.10.2015, Taipei, The 14th IFToMM World Congress, Oct/2015.
In this paper, a novel view on complex numbers and quaternions is presented by introducing a five-dimensional complex space which is defined as the ‘union’ of the complex plane C and the quaternion
space H. It is demonstrated how the complex 5-space can be visualized by R3 and by R2 for rotations with a fixed rotation axis. In these visualizations, the algebraic representations of a rotation, using a complex
number, quaternions, and a rotation matrix, appear in an elementary-geometric setup which is generalizing the unit circle. The definition of the complex 5-space is based on an explicit distinction of four different imaginary
units. The embedding of a rotation matrix into the three-dimensional view is achieved by the choice of an appropriate basis for the representing matrix of the rotation.
Rotational Displacements, Rotation Matrices, Complex Numbers, Quaternions