Hey guys, that concept is pretty interesting although that paper isn't easy for me to read. Apparently he's investiagting "completeness" of number representations in base-z where $\displaystyle z=-1+i$ or $\displaystyle 1+i$ or no? I found another reference that helps explain it:

http://www.academypublisher.com/jcp/...cp03026371.pdf

Couldn't help check this example: $\displaystyle 2007=1110000000001110011011101_{-1+i}$

That means $\displaystyle 2007=1(-1+i)^0+0(-1+i)+1(-1+i)^2+1(-1+i)^3+\cdots+1(-1+i)^{24}$

That's easy to check in Mathematica:

Code:

In[10]:=
val = 1110000000001110011011101;
alist = IntegerDigits[val];
Simplify[Sum[alist[[25 - n]]*(-1 + I)^n,
{n, 0, 24}]]
Out[12]=
2007

How about $\displaystyle 2007i=10000000011001101000111_{-1+i}$

Which I can check again in Mathematica:

Code:

In[29]:=
val2 = 10000000011001101000111;
alist2 = IntegerDigits[val2];
len = Length[alist2];
Simplify[Sum[alist2[[len - n]]*(-1 + I)^n,
{n, 0, len - 1}]]
Out[32]=
2007*I

. . . never did any of this in any of the computer science classes I've taken. Pretty cool.