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vectors are used to represent complex numbers, it helps visualize various sums/products. i and i correspond to real and imaginary axes.
Its cool you use your imagination this way, but like Q says, you have to ask yourself "to what end", how can you solve a problem or use your construct as a tool.
Its obvious what lining up vectors with an axes in mechanics does, or using spherical or polar coordinates to represent a problem, you have to create a use for your mapping construct or demonstrate that key properties hold and some theorems pop out (lol) about it. Otherwise good old cartesian solves a lot of problems and has a big body of math like analytic geometry, vector calculus, etc. ready to use it