Relationship between squaring a complex number and acceleration

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I know that the formula relating initial velocity, final velocity, acceleration, and distance is $v^2-u^2=2as$ and that squaring a complex number $v+u\mathrm{i}$ leads to $(v^2-u^2)+(2uv)\mathrm{i}$, so is there any reason why the two are so similar or is that just by chance?