Sorry to ruin the forum with hard sums, but I can't find the answer to this one.

if we have 4 numbers x,y,a and b where
Code:
e^y = e^a + e^b
i'm trying to prove that
Code:
e^(x+y) = e^(x+a) + e^(x+b)
however, x,y,a and b are not normal numbers, they are hypercomplex numbers (quaternions or larger) this means that we can no longer assume that a*b = b*a, and hence e^(a+b) is no longer e^a * e^b.

I can't test this as I can't calculate e^x for these numbers and I want to know If I can assume this Identity for non commutative numbers.

does anyone know anything about this?