# Transitive property with complex numbers

I'm having a debate with my friend. If real numbers a>b>c>d, can we say that a+bi > c+di? I think the answer is yes, and my argument seems to be confirmed by this post Order relation of complex numbers but even though I understand it, admittedly I'm struggling to explain in English why this relation is true. Can someone help me?

• No you cannot compare two complex numbers generally.. Mar 31, 2018 at 16:59
• The complex numbers are not an ordered field like the real numbers, so it does not make sense to compare them like this. See en.m.wikipedia.org/wiki/Ordered_field Mar 31, 2018 at 17:00
• Ok, thanks so much Mar 31, 2018 at 17:01

The only way we can compare complex numbers is through comparing their moduli (which is a function from the complex numbers to the real numbers), however since this loses information about the complex numbers (since $|1+i|=|1-i|=|\sqrt{2}i|=\cdots$), it is not so useful to us.