Real numbers have a unique canonical ordering (up to isomorphism). So given x and y real, it is always true that either x < y, x = y or x > y. Complex numbers d

Real numbers have a unique canonical ordering (up to isomorphism). So given x and y real, it is always true that either x < y, x = y or x > y. Complex numbers don't have a unique ordering. So for for example take 1+i and 5-2i. Which is bigger? There are many possible orderings that you can define on the complex numbers. The fact that ordering them is not unique means that any such order is a choice rather than a property of the numbers themselves. You're thinking about measuring distances in the complex plane which is absolutely fine, and also has a canonical definition. I was referring to the fact that it's not intrinsically meaningful to say that 'London is (5000+250i)km from New York'