Inequalities between a real number and an imaginary number

1. Jun 4, 2012

phosgene

1. The problem statement, all variables and given/known data

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.

2. Jun 4, 2012

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.

3. Jun 4, 2012

HallsofIvy

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

4. Jun 7, 2012

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 :)

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook