I’m aware of that identity. There’s a good chance I misunderstood what she said about it being just a notation.

This very nice Romanian lady that taught me complex plane calculus made sure to emphasize that e^j*theta was just a notation.

Then proceeded to just use it as if it was actually eulers number to the j arg. And I still don’t understand why and under what cases I can’t just assume it’s the actual thing.

What was the issue there ?