Expansion of Complex Number
2005jbk | Y. A. Furman, A. V. Krevetsky  // Mari state technical university, Yoshkar Ola, Russia

The expanded complex numbers are introduced by means of imaginary unit $i$ replacement by one-dimensional on multivariate $3D$ or $7D$ imaginary unit $r$. It is shown, full quaternions and octaves appear as a result of a turn around the material axis $0Re$ plane where $a+ib$ number is set in $4D$ and $8D$ spaces. Rotor-complanar classes of quaternions and the octaves appearing as a result of similar transformations are considered. They represent commutative-associative algebras.

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