Say there's some function, f(n), that is the multiplicative inverse of n*0. Thus, $\frac{f(n)}{0} = n$.
We know by inspection f(n) is not real.
And to stay consistent with existing models, we know n*0 has a real part 0.

Therefore, you could say $n*0 = 0+f(n)$.
But when we try to divide through by zero, we get:

$\frac{n*0}{0} = \frac{0}{0} + \frac{f(n)}{0} = 1 + n$

Does it make more sense to say

$\frac{n*0}{0} = \frac{0}{0} + \frac{f(n)}{0} = 0 + n$, where $\frac{0}{0}=0$

Or rather

$\frac{n*0}{0} = \frac{0}{0}+ \frac{f(n-1)}{0} = 1 + (n-1)$, where $\frac{0}{0}=1$?