[shou4577]

I have mixed feelings about this explanation.

On the one hand, the mathematician inside of me is raging "this is neither specific, nor rigorous!" In my opinion, this definition is as close to useless as a mathematical definition can be, since the person who has this (and only this) will be hard pressed to answer any other questions involving complex numbers. For example, what is multiplication by i+1? Without further understanding, I don't think such a question can be answered.

On the other hand, the teacher in my head is celebrating. This person managed to take a concept normally feared and hated by the population at large and made it interesting and understandable. The response is well thought out, and is much more engaging to the reader than any response that I could come up with. In short, this explanation is more likely to make the person interested in mathematics, while a more technical definition would probably just make them zone out.

What do other people here think about this? Is the clarity and interest worth the loss of utility? Am I totally off base?

[egsmith]

I would argue something is better than nothing. And if this gets people to start using the tool then maybe they will start to hit the cases where the loss of utility matters, and then this can be the source of inspiration to actually tough out the technical inspiration. Probably a long shot in general but it worked that way for me.

[agumonkey]

What I love about it is the by-necessity introduction. Limits of previous concepts drive the next idea, I believe that it's a very efficient and general approach to communicate.

[Almaviva]

> For example, what is multiplication by i+1? Without further understanding, I don't think such a question can be answered.

i+1 on the plane is a vector at 45 degrees and a scaling of sqrt(2). So multiplying by it scales your multiplier and rotates it 45 degrees. This is a direct extension of the intuitive understanding given.

[gizmo686]

As a math student I can say that if the teacher explains something in a way that