A tessarine is a hypercomplex number of the form
 |
where 
, 
, 
,
and 
are real
numbers and
 |
Tessarine multiplication is commutative and associative. The algebra has zero divisors,
since 
. It contains the two-dimensional
subalgebra 
, in which 
; this is the algebra of split-complex numbers. The tessarine algebra
is isomorphic, as a real algebra, to the modern bicomplex
numbers and to the direct sum 
of two copies of the complex
numbers.
