What are the uses of split-complex numbers? The set of Complex numbers can be used in lots of domains like geometry, vectorial calculations, solving equation with no real solution etc. But what are the uses of split-complex number that can't be done with complex numbers? I think you could do the same works in geometry or vectorial calculation in a "split-complex" plane but what advantages gives us to know that j is a solution of the equation $x^2=1$?
What I've thought so far is that using complex numbers and split-complex numbers together, we can have numbers of the form $a+bi+cj$ so everything that can be done in the complex-plan could be extended to 3 dimensional space by adding a split-complex part.


What I've thought so far is that using complex numbers and split-complex numbers together

You will get exactly tessarines, a commutative associative algebra. But it is 4-dimensional: $ij$ is a separate unit, similar to complex unit. $i^2=-1$, $j^2=1$, $(ij)^2=-1$.
So, your number will look $a+bi+cj+dij$ or $(a+bi)+j(c+di)$ or $(a+bj)+i(c+dj)$.
