Physics

Took me a really long time to realize complex numbers aren't necessarily "complex", but that they represent system parameters in a "different" phase space with extra data, where you can map the phase space 1-to-1 to the original system.

This is a really good recent SIAM that explains complex solutions to spring systems, where in the complex phase space, you can just imagine a "rocket" that spins around the end of the spring at fixed rotational speed.

It's almost always better to learn the system and these solutions in the complex space phase space!

Took me a really long time to realize complex numbers aren't necessarily "complex", but that they represent system parameters in a "different" phase space with extra data, where you can map the phase space 1-to-1 to the original system.

This is a really good recent SIAM that explains complex solutions to spring systems, where in the complex phase space, you can just imagine a "rocket" that spins around the end of the spring at fixed rotational speed.

It's almost always better to learn the system and these solutions in the complex space phase space!

https://www.siam.org/publications/siam-news/articles/geometry-of-the-phase-lag/