If you think about this for long enough, you should suddenly understand why e to the i pi is minus one. In fact it’s just a really obvious thing that has to be true. At that point you’ve probably got it.
Be careful about the illusion of transparency here. This all strikes me as the sort of stuff that is unlikely to be obvious.
Sorry, obvious to a mathematician who thinks about dz/dt=iz and realises that “exponentiation is time-evolution”. At that point it’s just “if you rotate for just long enough to turn half-way round, you’ll be pointing backwards”.
Be careful about the illusion of transparency here. This all strikes me as the sort of stuff that is unlikely to be obvious.
Sorry, obvious to a mathematician who thinks about dz/dt=iz and realises that “exponentiation is time-evolution”. At that point it’s just “if you rotate for just long enough to turn half-way round, you’ll be pointing backwards”.