and also ELI16 what a an imaginary number is and how it works in real life
In: Mathematics
Some problems are complex enough that a point can’t be represented by just one number, it needs two. You can imagine it like a point on a graph. For these “2D numbers” to be useful, you need to define how to add and multiply them in a way just like regular numbers. The way the rules shake out, (0, 1) * (0, 1) = (-1, 0). The y axis is called the “imaginary numbers” (using the letter ‘i’) and the x axis behaves just like the regular real numbers, so you can write it as i * i = -1.
Basically, the moment you start talking about imaginary numbers, you’re actually talking about these “2D numbers” (complex numbers), which is a different system than the regular 1D numbers (real numbers) we usually work with.
They’re really good for problems involving waves and transformations. For example, multiplying by (0, 1) rotates your complex number by 90 degrees!
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