I disagree, it's not simply arbitrary. Euler's formula eⁱˣ=cos(x)+i⋅sin(x) exists outside of any physical representation of the complex plane. And the fact th

I disagree, it's not simply arbitrary. Euler's formula eⁱˣ=cos(x)+i⋅sin(x) exists outside of any physical representation of the complex plane. And the fact that we already graphed trigonometic functions lent itself naturally to a corresponding graph of complex functions. As sibling comments have stated, any graphical visual representation of completely independent variables is most efficiently represented with perpendicular axes, so the mapping is inevitable.