- #1

Anixx

- 80

- 12

I just wanted to share that there is a way to easily implement split-complex numbers (and tessarines) in Mathematica.

Code:

```
$Pre = If[FreeQ[#, J], #, Module[{tmp},
tmp = Evaluate[
MatrixFunction[Function[J, #], {{0, 1}, {1, 0}}]] //
FullSimplify;
tmp /. {{a_, b_}, {b_, a_}} -> a + J b]] &;
```

After this code you can use split-complex unity J in any functions. I recommend to try

Code:

```
J^I
I^J
J^J
Log[J]
Sqrt[J]
Gamma[J + 2]
Zeta[J + 1]
PolyGamma[J + 2]
Exp[J]
(-1)^J
2^J
```

Have fun!