Expert: Scott A Wilson - 1/24/2010

Question
In a complex inequality is m<-3 or m>3 a no answer ?

Answer
In complex number theory, there is almost always an answer to an equality.
However, for inegualities, they don't really apply.

In complex math, the vector space is a two dimensional plane.
The x direction is treated as the real part and the y direction is treated as the imaginary part.

The < or > symbol could be applied to the real part or the imaginary part, but not both.
For example, how do 1+2i and 2+i compare?  In the real direction, the 2nd one is greater.
In the complex direction, the 1st one is greater.

If both number were converted to polar, they would both have the same r value.
For one, theta = artcan(2) and for the other, theta = arctan(1/2).
So in complex numbers, the value of r would be equal, but the 1st would have a greater angle.

Still, from what I've seen, the < and > symbols are used on a line tat is full of real numbers.