They say that math and science are connected but......

You are correct about imaginary numbers. They exist to allow for negative square roots to happen. What is even more interesting perhaps is this:

e^ix = cos x + i*sin x

It's the identity used to solve the differential equation I discussed in my post.

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If you're in high school, yes that's how it will be. But if you go into a science based major in college, like physics or engineering, you will undoubtedly fail every science course if you don't have a handle on the corresponding math. You won't spend hours observing, you will now be proving what caused your observations, or providing mathematical proofs for common equations like E=mc^2 .

Since you aren't really catching the link with math, chances are you are still learning the basics and how to manipulate stuff as opposed to applications and theories.

Well, science only uses math as a tool. That's the important part here, it's only a tool to model the universe around us. I don't know if you've taken calculus yet, but there are a lot of overlapping subjects between calculus and physics. Some examples include second derivative and acceleration, first derivative and velocity, flux and flux in E&M, etc.

Assuming you're in hs, otherwise you should really go somewhere else.

in Hs and bellow most science is sort of presented in a "fun facts to learn" kind of way, in large part because the math of science is calculus and differential eqns. and you have to do algebra first so that it makes sense. Biology especially contains some pretty involved math that most schools dont teach because there isnt enough time to teach the background info, for example fractals.