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GalFisk t1_jee40gx wrote

Reply to comment by gg_wellplait in ELI5 Why does a Minus Negative turn into a Plus? by doggie_doggie

With imaginary numbers. They go up and down instead of left and right. If you combine them with real numbers, you get to do math in two dimensions.

I don't know a lot about what it's good for, but I know it has its uses.

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Isolus_ t1_jee7el1 wrote

You could even go two dimensions further and use quaternions...

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GalFisk t1_jee7h79 wrote

Cool, what are those good for?

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Isolus_ t1_jee8pvb wrote

They are often used to describe rotations in the 3D world. So when you have a camera drone (multicopter) there is a good change that they are used to process the sensor inputs (gyroscope/accelerometer) and calculate the corrections needed for a stable flight.

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GalFisk t1_jee92xq wrote

I saw a video on that. They had arrows pointing right, up and front, and connected them end to end in order to make a new arrow that pointed to the destination. Are quaternions the same as making calculations using x, y and z coordinates?

They also used trigonometry to transform back and forth between coordinates and angles.

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Isolus_ t1_jeeeqwy wrote

There are different ways to achieve this and it's hard to say what you have seen. The "classical" and "easy" approach is to use vectors and apply rotation matrices. But for a flying device you often rotate around an arbitrary axis and not around x, y or z. That is where quarternions come in handy. They can represent a rotation around an arbitrary vector. But they are harder to understand so most teaching of those concepts is done the "classical" way. Quaternions are also numerically stable. Computers can only represent an approximation of a number (for example you can't store Pi, only the beginning). Using matrices it's happens more easily that an error introduced through these approximations changes your result a lot.

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