Here is my 2003 study of Bicomplex Numbers 'The Complex Number Theory of Minkowskian Geometry and the Quaternion Algebras'.
Please download (by clicking Bicomplex.pdf below) :
Note: this paper was first published 3rd January 2003, on my website www.geocities.com/timsheltonjones/maths/cq02.html - now demolished (thanks Yahoo!).
The original can still be viewed in this web archive : http://web.archive.org/web/20090829122122/http://geocities.com/timsheltonjones/maths/cq02.html