Complex numbers inequalities and optimisation I'm now aware that you can't definitely with ease say that one complex number is greater than another. 
Though what about imaginary numbers? Is $5i > 3i$? Is $i>-i$?
Is it possible to optimise (find the minimum or maximum) of a complex number function? I assume if it's not ordered you can't do that ,as when we optimise for real numbers the question is if which is the greatest or least output. But if you can't say one output is greater than another than how would you optimise it?
Thanks

I Think we can't say that 5i>3i.
But if the modulus is greatest then we say the complex number is greater.|5i|=5 &|3i|=3. So we may say that 5i>3i. But it is true that we can't say that 5i>3i
