I said it before I will say it again. HOW is it that I learned to balance a check book in jr high AND high school but no other schools seem to teach it? It was even in math class where I learned it.
I asked my teachers and they said they don't teach it because they believe that check books and taxes are something your parents should be teaching you at home. My schools didn't have drivers Ed either.
I've never understood the use of imaginary roots and I haven't used them at all through my calculus career. If I had to guess, they are used in Linear Algebra or Differential Equations.
I use them every single day and if we hadn't invented them my work would be ten times harder. They are used to transform trigonometry into algebra, which is something you always want. Electromagnetism without complex numbers is pure torture.
You can represent a propagating plane wave with a cosine, but as soon as you want to take into account things like absorption you need exponentials. When working with complex numbers, everything is exponential, no more cosine. Many concepts merge into one elegant framework. My thesis has a chapter on the subject if you're curious :D.
While I am curious, I am also on break lol. But it does sound interesting. We didn't do much in absorption with electromagnetic spectrum. We did reflection and refraction but nothing else.
I love this one because balancing a checkbook is literally one of the first things you learn in math: basic addition/subtraction. If you're in high school and you can't balance a checkbook, you really need to get your act together.
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