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What they are asking is to show that no relation $<$ can exist that complies with the order axioms, i.e.:
In this case, if we take $i > 0$ we get $i^2 = -1 < 0$, contradicting (4). So by (1) it must be $i < 0$. But $i^4 = 1 > 0$, again contradicting (4). So no relation $<$ can exist on $\mathbb{C}$ which complies with (1) to (4).
try z = i the square root of -1 for a simple contradiction.