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The_camperdave t1_j6c4gmm wrote

Reply to comment by squigs in ELI5: Why do imaginary numbers even need to exist? by Tharsis101

> Essentially, numbers give us forward. Negative Numbers give us backwards, and imaginary numbers give us "sideways"

So what gives us a vertical? SQRT(-i)?

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squigs t1_j6c9r2c wrote

This is where my answer is a bit messy. Imaginary numbers can be thought of that way, but using them for 2d space is an application.

We do have quaternions. This gives us 3 imaginary numbers, we call i, j and k, where squaring any of them gives -1, and ij = k, jk = i and ki =j. Weirdly, we lose commutivity here. ij = k, but ji = -k. Reversing the order gives a negative result.

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