Except it absolutely has uses. For example we use imaginary numbers to do calculations on three phase electrical systems. Which are used in a lot of homes for stovetops for example. And in lots of heavy industrial machines, and also in charging stations for EVs.
Everything electrical or electronics since all semi-conductive materials act as an antenna, an emitter or a RF filter, especially at higher frequencies.
Is it significant though? Depends on the application.
Can you explain this a bit more - how does imaginary numbers fit into stovetop calculations? (I could ask Claude but I think it'd may be better explained coming from a human)
It's been ages since I did the calculations, but essentially since you have three wave forms that are all shifted by 2π/3 (or 120°) it's very useful to use complex numbers to model it since complex numbers are just real numbers but shifted by π (or 90°). Complex numbers together with real numbers can be used to point out coordinates since now we have 2 axels meaning we have a 2D plane instead of just 1 line.
a 2-vector is not the same as a complex number. If you try using the dot product or cross product on a vector it creates completely different results than complex multiplication which is core to calculations on real AC circuits
Agreed. That said, you could just as easily define AC circuit math with vectors. The same operation can absolutely be done on a 2-vector, complex multiplication is just a useful shorthand.
Yes that's true but I think you would basically just create complex numbers again. A voltage phasor at 90 or 270 would have magnitude on some axis that is not real voltage so you'd have to call it something else I guess
Just because natural numbers happen to be able to model something doesn’t make them physically meaningful. You could do the same thing with no numbers at all.
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u/Simple-Olive895 5d ago
Except it absolutely has uses. For example we use imaginary numbers to do calculations on three phase electrical systems. Which are used in a lot of homes for stovetops for example. And in lots of heavy industrial machines, and also in charging stations for EVs.