I majored in math and took a course on waves through the physics department. Everyone struggled with why imaginary numbers would show up and I was just like "we

I majored in math and took a course on waves through the physics department. Everyone struggled with why imaginary numbers would show up and I was just like "we took the square root of this negative number, and the reals aren't closed when we take square roots, therefore imaginary." I missed out on a lot of physical intuition and had basically no concept of what the imaginary numbers actually meant