What complex numbers are and what they are used for.
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The words complex and imaginary that usually get assigned to this concept are really poor names unfortunately. They tend to make people think they aren’t real or complicated or esoteric.
Complex numbers can be thought of as 2dimensional numbers. Just like how on graph paper you can measure how far left-right you are AND up-down you are from point to another, you can do the same with complex numbers. That’s all they are. Instead of having a number line, you now have a number “grid” or plane to be more technical.
They are used everywhere amazingly enough. You’ll find that some of the most common applications is for things that oscillate or rotate. There are ways to describe this behavior as rotations in complex numbers. Turns out, a lot of stuff oscillates and rotates in one way or another. There’s even math you can do that allows you to describe ANYTHING (even if it’s not oscillating) as some combination of oscillations and rotations. So the applications are practically endless. To name some concrete examples and further reading terms: quantum mechanics, Fourier analysis/transformation, electrical engineering
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