And by the way Maxima, Maple's mommy, thinks (by default? not sure if it's possible to change this behaviour) that 0^0 should generate an error. It also throws a different kind of error for 0^z for z complex. It's not as universal a convention as you might think.

Huh? But why would 0^I be a division by zero error? Maple also thinks that log(0) is a division by zero, though perhaps it would be better to claim a domain of definition error in the log function. Why is 0^(1+I) not equal to (0^1)*(0^I)? How is Maple evaluating these two? It looks like it's taking limits of the type ε^z as ε → 0 in each case.