# Show that it is impossible to order C (complex numbers) so that it becomes an ordered field.

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Hint: what happens when you multiply both sides of the inequality by $i$?

Clarification:

To begin, suppose that $i>0$. Then since $i>0$, we can multiply both sides of the inequality by $i$ to get $i^2 >0$ (the inequality doesn't flip because $i>0$). Why is this a contradiction?

Now, what happens when we assume $i<0$?

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### arielle

Updated on July 21, 2022