and also ELI16 what a an imaginary number is and how it works in real life
In: Mathematics
Just to offer another perspective here, if you’re interested in real-life applications of imaginary numbers, a good example is Electricity… specifically how Alternating Current works.
The characteristics of various loads on our electrical grid mean that almost all AC power has both an Active and Reactive component. Active power is what you’re used to seeing, such as for purely resistive loads like lights or running your toaster. But plenty of loads also have capacitive and inductive components, such as motors, transformers, electronics, etc. This means that the alternating current passing through these kinds of loads leads to a mismatch between the current and voltage waveforms, resulting in the need for what we call Reactive power.
Some people like to call it “imaginary” power because the math that allows you to easily calculate these reactive characteristics heavily involves imaginary numbers (though in electrical engineering we use the letter “j” instead of “i” and I’m not entirely sure why). But of course, there’s nothing imaginary about it. Reactive power is just as “real” as Active power, it just serves a completely different function. It also disappears completely when we’re talking about DC circuits instead.
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