> Or are you arguing that you should always try and teach complex numbers and the Euler identity to avoid strained analogies?
I think it’s okay to be explain complex numbers. I think it’s just best to additionally explain why. That is, show why (real, imaginary) is a better numerical system than the more broadly taught (x,y) of the 2 dimensional space being explored.
As for the Euler identity I suppose you could include that when explaining why we use the exp() function, which is because it plays nicer with integration and derivation than other numerical representations.
I want the analogies to be representative of the work rather than my own mental model of it.
I think it’s okay to be explain complex numbers. I think it’s just best to additionally explain why. That is, show why (real, imaginary) is a better numerical system than the more broadly taught (x,y) of the 2 dimensional space being explored.
As for the Euler identity I suppose you could include that when explaining why we use the exp() function, which is because it plays nicer with integration and derivation than other numerical representations.
I want the analogies to be representative of the work rather than my own mental model of it.