> I find I don't really need to remember trig as long as i remember how imaginary exponentials and the unit circle works.
Or, to phrase it differently, trigonometry is just a different language for the restriction of the complex exponential to the imaginary axis, and you are remembering the facts in translated form. (Which I agree is much better—it's certainly the only way I can ever remember the thicket of identities! But I'd argue that it's still remembering trigonometry.)
Def agree on Stirling's though.