I teach maths and one of the analogies is use is watching a film of someone walking forwards and backwards. If you play the film forwards (multiplying by positive), you can see the person walking forwards and backwards as normal. If you play the film backwards (multiplying by negative) you see the opposite. So multiplying by negative reverses whatever was happening before. Hard to put into words but the visuals (hopefully) seem to explain it well enough.
That’s surprisingly accurate, as people here are highlighting (it makes geometrical sense when dealing with complex numbers).
My nephew once asked me this question. The way that I explained it was like this:
It’s a different analogy but it makes intuitive sense, even for kids. And it works nice as mnemonic too.
I teach maths and one of the analogies is use is watching a film of someone walking forwards and backwards. If you play the film forwards (multiplying by positive), you can see the person walking forwards and backwards as normal. If you play the film backwards (multiplying by negative) you see the opposite. So multiplying by negative reverses whatever was happening before. Hard to put into words but the visuals (hopefully) seem to explain it well enough.
Its good maths but terrible realpolitick.