Actually, even the definition of this form requires i, because it's e^(i)(pi/2) = i. The simple assumption that sqrt(-1) = i is problematic because you can ge

Actually, even the definition of this form requires i, because it's e^(i)(pi/2) = i. The simple assumption that sqrt(-1) = i is problematic because you can get something like i^2 = (sqrt(-1))^2 = sqrt((-1)^2) = 1. The wonder and surprise of complex numbers is that assuming seemingly arbitrary properties of a constant like i lead to a number of deep and beautiful results.