# Inequalities between a real number and an imaginary number

## Homework Statement

I'm just having a problem with a step that's part of a larger problem. Specifically, if I have:

$\sqrt{2}i\leq\sqrt{2}$

I'm not sure what this actually means. If I ignore the i, each side is the same distance from the origin if I imagine both points on a graph, implying that both sides are equal. But I don't know whether this is a correct interpretation.

## Answers and Replies

I don't think without a definition of ##\le## for complex numbers, that means anything, and there isn't a generally accepted one. Perhaps try to solve your problem a different way, or try to figure out what ##\le## means in the context of this problem.

HallsofIvy
As whovian said, the set of complex numbers is NOT an ordered field. Perhaps you intended absolute values? $\left|\sqrt{2}i\right|= \sqrt{2}$.