A split-complex number, also called a hyperbolic number, has the form
 |
where 
and 
.
Addition and multiplication make the split-complex numbers a two-dimensional commutative algebra over the real numbers.
This algebra is not a field,
since 
,
so 
and 
are zero divisors.
The map 
identifies the split-complex algebra
with the direct sum 
. The image is an ordered
pair, not a choice between the two numbers 
and 
, and the inverse map sends the ordered pair 
to 
. Under this identification, addition and multiplication
are performed componentwise. In particular, 
maps to 
, which is distinct from both 
and 
even though 
. The tessarine and bicomplex
number systems each contain a copy of the split-complex numbers.
