[sannee]

I am an EE and our complex analysis class definitely did define complex numbers "rigorously" (in the usual R^2 with multiplication -> wow, it's a field way, none of the fancy algebraic closure stuff).

However, later I spoke with some of my classmates and it turned out that this left absolutely zero impression on them and they still believed that "we define i to be sqrt(-1)" high school rubbish...