I have never been totally satisfied by the explanations for why e to the ix gives a sinusoidal wave.

What about n=3?

3√-1

Exactly. Wouldn't that be -1?

The comic implicitly specifies thag it's *multiplied* by √-1, not the nth root of -1.

Oh, got it.

Surprised this still conveys the same exact message if you read the dialogue in order of character speaking ordered from left to right:

"Numbers of the form n√-1 are imaginary, but can still be used in equations."
"And e^(π√-1) = -1."

"Okay."
"Now you're just f**king with me."