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Inequality of complex numbers 
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#1
May514, 04:26 AM

P: 63

Are the less than (<) and greater than(>) relations applicable among complex numbers?
By complex numbers I don't mean their modulus, I mean just the raw complex numbers. 


#2
May514, 05:33 AM

P: 997

The short answer is "no". The greaterthan and lessthan relations do not apply.
A longer answer is that the complex numbers together with the standard operations of addition and multiplication form a "field". But there is no greaterthan relation that can be used to make it an "ordered field". http://en.wikipedia.org/wiki/Ordered_field The problem comes when you try to decide whether i is positive or negative. i is different from zero, so it has to be either positive or negative. If it is positive then i*i must be positive. But i*i=1 and 1 is negative. If i is negative then i must be positive. So i*i must be positive. But i*i=1 and 1 is negative. 


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