Here http://farside.ph.utexas.edu/teaching/301/lectures/node89.html
They use complex analysis to derive the equations of non-uniform circular motion.
My confusion is this: In the derivation they basically say that unit-vector r is equal to e^(itheta) and unit-vector theta is equal to ie^(itheta). While I do understand that they have a very similar geometrical meaning, I don't know how you can say "they're equal". It just doesn't make sense forme me that you can set up an equality here.
How is that they're equal?
I'm starting to think that perhaps they're not equal (because they never explicitly say so) but it's just a very useful analogy, or something like that.
Thanks a lot, and I hope my question is not unclear. BTW, complex numbers are new for me so I'd appreciate if you don't use really advanced jargon. Thanks again.