Notably, neither `1 + i > 1 - i` or `1 + i < 1 - i` are correct statements, and obviously `1 + i = 1 - i` is absurd.

chongli 5 hours ago | parent | next [-]

What do > and < mean in the context of an infinite 2D plane?

yifanl 5 hours ago | parent | next [-]

Typically, the order of complex numbers is done by projecting C onto R, i.e. by taking the absolute value.

	▲	chongli 5 hours ago \| parent [-]
		Yes I’m aware. It’s a work around but doesn’t give you a sensible ordering the way most people expect, i.e: -2 > 1 (in C) Which is why I prefer to leave <,> undefined in C and just take the magnitude if I want to compare complex numbers.

layer8 5 hours ago | parent | prev [-]

One is above the plane and the other is below it. ;)

bell-cot 2 hours ago | parent | prev [-]

In a word - "true".

In more words - it's interesting, but messy:

> The complex numbers also cannot be turned into an ordered field, as −1 is a square of the imaginary unit i.