Inequalities between a real number and an imaginary number

[phosgene]

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.

 

[Whovian]

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? $\left|\sqrt{2}i\right|= \sqrt{2}$.

 

[phosgene]

Sorry, yes, I forgot to include the absolute value signs! But it turns out I got a previous step in the problem wrong, anyway...so I'll just post a different topic on the whole thing. Thanks for the replies though :)