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:
- the friend of my friend is my friend; (+1)*(+1) = (+1)
- the enemy of my friend is my enemy; (+1)*(-1) = (-1)
- the friend of my enemy is my enemy; (-1)*(+1) = (-1)
- the enemy of my enemy is my friend; (-1)*(-1) = (+1)
It's a different analogy but it makes intuitive sense, even for kids. And it works nice as mnemonic too.