>>10928289>>10928278haha yeah thats way over my head
i found an interesting example of a DE in a form
y" + y = 0
cos"(x) = - cos(x)
sin"(x) = - sin (x)
so both sin and cos are the solutions.
and so are e^ix and e^-ix.
since the 2nd derivative of e^rx is r^2e^rx
so we get r^2e^rx + e^rx = e^rx(r^2 + 1) = 0
since e^rc cannot be zero we have to solve
r^2 = -1.
and that's how it can be introduced as sqrt(-1).
So apparently the connection is both trig functions and e^jx describe harmonic motion or something like that.
I think of it this way:
y" = - y
If it is about motion along a path, the 2nd derivative is acceleration. When cos is at the positive peak, the acceleration becomes negative, so it is going down and when it reaches the negative amplitude peak, it changes the direction. So cos is a solution as a simple harmonic motion. Is that about right?
>>10929153kek i posted there about complex numbers in the context of AC analysis in the /ohm/ thread. it resulted in a long autistic exchange.. but it was awesome and helpful. there are /sci/ tourists there as well.
