I thought this was similar to mapping vectors to complex numbers. Many of you have probably done this in high school math, mapping vectors to complex numbers, multiplying them in the space of complex numbers, and then putting the resulting new complex numbers back into the vectors again. Multiplication in the space of complex numbers is a rotation back into the space of vectors. There are differences in ease of doing this in different spaces. In high school math, it was easier to multiply complex numbers than to rotate vectors.
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