I walk in the x direction, if I walk twice as fast, 2x, if I walk backwards, -x. What about ix? If I say that I walk an imaginary distance ix then this means in physics and maths that I walk perpendicular to the direction of x (there must be a new dimension).
If I scale an object by 2 in it's x dimension then it doubles in size, if I scale an object by -1 then I invert it. What happens when I scale an object by i? Then I change it's size in the direction perpendicular to x.
It appears to me that imaginary numbers are used to describe things happening in the dimensions that are orthogonal to the dimension being considered. It could be error away from a line, or another effect like magnetism acting perpendicular to the observed effect, it is about the actions perpendicular to the dimension being considered?
Is this a correct way to understand it?
If there are many perpendicular dimensions can they all be described by one single complex dimension? Do we transfer the information from many orthogonal dimensions into one complex dimension for ease of seeing how all the other dimensions in the system interact with the dimension we are studying?