What is the use/need of complex numbers in real life if they are imaginary?
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Video games! Complex numbers map really well to rotations!
See, when you describe rotations in 3d, its easy to use spherical coordinates:
an example would be:
spin to face your target, (y rotation)
raise your arm to aim a gun, (x rotation)
rotate your gun so you look like a gangster. (z rotation)
That works really well if your making a ground based shooter.
But what if you are making a space based game?
You would have no frame of reference to rotate the ship by.
This is where you use something called a transform matrix
its a 4 by 4 grid of numbers that accurately describe the rotation/scale/position of something.
However, theres a lot of extra information there thats not needed if you just want to control the rotation of a spaceship. And when you are making computer games, efficiency and space matter.
Instead, you would use something called a quaternion.
A quaternion is a number that has:
1 part real and 3 imaginary parts.
Where Complex numbers have the definition i*i = -1
then you add in j*j = -1, and k*k = -1, and most importantly: i*j*k = -1
This creates an extended imaginary system, that is ideal for working with rotations in 3D video games.
Most space, and some underwater games will use quaternion, and a lot of game engines use quaternions under the hood for other stuff
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