I know this may very well be a silly question. I always hear that Complex numbers cannot be ordered. But there's something I'm missing... Why can't we just compare two complex numbers $z_1,z_2$ as follows:
A number is less then the other if the modulo is less or equal modulo but angle less from the x axis, in other words $z_1$<$z_2$ if $\rho_1<\rho_2$; or $\rho_1=\rho_2$ and $\theta_1<\theta_2$ where obvously $$z_1=\rho_1 e^{i\theta_1}, z_2=\rho_2 e^{i\theta_2}, \mathrm{with\ }\theta_1,\theta_2 \in [0,2\pi)$$
Why don't we do it? And if we do, why everyone always says that the Complex numbers cannot be ordered?