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) |