For what it’s worth, my first session went like this:

  >> e^iπ+1
  2.6974097548 + 2.6435590641i
  >> e^iπ
  1.6974097548 + 2.6435590641i

In fairness, I still don’t know where “e” comes from in complex number notation. The transition from cos(angle) + i sin(angle) seems to become “e^i(angle), lol” and no one explains it further. Before I started doing signal processing, I too would have thought that e^i pi is something like 1.69 + 2.64, so it’s correct, in a certain sense. But perhaps not the common mathematical sense.

EDIT: Ah, I see the problem. I suspected that e^iπ was being turned into πe^i incorrectly, but when I typed the open parenthesis for e^() and put my cursor inside it, typing "i" resulted in e^i() rather than e^(i). So it was impossible to parenthesize correctly, and I assumed e^iπ had the usual meaning.