On the one hand, I agree with you. On the other hand, to answer your demand: I define complex exponentiation by the formula e^(it) = -1 for all real, nonzero t

On the one hand, I agree with you. On the other hand, to answer your demand: I define complex exponentiation by the formula e^(it) = -1 for all real, nonzero t. Clearly stupid. Why? There are a lot of properties that one might naturally ask e^(it) to satisfy (for example, that e^(it) * e^(iu) = e^(i(t + u)), or that its derivative is ie^(it)), and the usual complex exponential satisfies all the right ones. So writing e^(i * pi) with no context has, I submit, at least some content.