Bicomplex number

A bicomplex number is a number written in the form, a + bi₁ + ci₂ + dj, where i₁, i₂ and j are imaginary units. Based on the rules for multiplying the imaginary units, then if A = a + bi₁ and B = c + di₁, then the bicomplex number may be written A + Bi₂. Thus, bicomplex numbers are similar to complex numbers, but the two parts are complex rather than real. Bicomplex numbers reduce to complex numbers when A and B are real numbers.

Multiplication of bicomplex numbers is both commutative and associative and distributes over addition. Given this and rules for multiplying the imaginary units, any two bicomplex numbers may be multiplied. Multiplication of the imaginary units is given by:

• i₁ · i₁ = -1
• i₂ · i₂ = -1
• j · j = 1
• i₁ · i₂ = j
• i₁ · j = -i₂
• i₂ · j = -i₁

External links

• http://www.3dfractals.com/bloch/node2.html