I am going into Honors Algebra II and while I am fine at using imaginary numbers in a formulaic sense I never understood them conceptually. I can’t tell if they exist just to make math work better or because there is an actual logical way to understand them
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You need imaginary numbers to describe waves or, rather, sinusoids. And sinusoids are fundamental to soooo many things. Why? Well, technically it’s because they are the eigenvectors of a series of differential equations. but more simply put, they are the solution to most math problems that involve rates of change. That includes electricity, photonics, thermodynamics, fluid mechanics, structural analysis and so forth.
why are imaginary numbers needed for wave equations, well you need something that cycles when multiplied by itself. keep multiplying i times i and you’ll go through 4 values. That’s the part that’s used to describe a wave.
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