TABLE A1
Summary Table with the Basic Properties of Bicomplex Numbers
| Name | Definition | Reference | |
|---|---|---|---|
| Bicomplex numbers |  | (Alpay et al., 2014, p. 10) | (A.1) |
| Bar-conjugation |  The terms multiplying i and k are negated | (Alpay et al., 2014, p. 10) | (A.2) |
| †-conjugation |  The terms multiplying j and k are negated | (Alpay et al., 2014, p. 10) | (A.3) |
| Conjugation |  The terms multiplying i and j are negated | (Alpay et al., 2014, p. 10) | (A.4) |
| Conjugation properties | Each conjugation is additive, involutive, and multiplicative | (Alpay et al., 2014, p. 11) | (A.5) |
| i-modulus |  | (Alpay et al., 2014, p. 11) | (A.6) |
| j-modulus |  | (Alpay et al., 2014, p. 12) | (A.7) |
| k-modulus |  | (Alpay et al., 2014, p. 12) | (A.8) |
| Idempotent decomposition |  | (Alpay et al., 2014, p. 15) | (A.9) |
| | · |k idempotent decomposition |  | (Alpay et al., 2014, p. 21) | (A.10) |