I'm English. In USA you say math, in England you say maths or mathematics and statistics etc.

That's interesting. I mean, we say statisticS and mathematicS too, so really we should say maths (we do say stats, by the way, and not stat). But it sounds weird... anyway.

Is that degree level? Did you get that off wikipedia, or did you already know it?

Its something I learned/figured out* in my complex variables class, which is pre-graduate level class. I am currently over halfway done with completing my Math major in college. Wikipedia can sometimes be helpful with math, but often their proofs of concepts are very bad, or they assume that the reader has a PhD in math.

*in higher level math classes you have to figure out as many things as you are taught. Which can be both rewarding and annoying.

Wow this is beyond my knowledge.

Well, maybe! But I don't think it is beyond your

*understanding*. If you think of the sphere as a ball placed on the origin of the plane, and then wrapping the plane around the sphere, it kind of makes sense. All of the "edges" of the plane (ie the points infinitely far from zero) would meet at the top of the ball.

Notes that this also implies that all lines can be thought of as circles through infinity.

More importantly it gets more difficult to determine if you have a negative decimal imaginary number

What's really weird is when you compare real numbers and pure imaginary numbers.

For instance, which is greater: i, or 1?

For reasons such as these, we don't try to compare sizes of complex numbers. Instead, we compare sizes of their absolute values, which is just their distance from the origin in the complex plane (just like how with real numbers the absolute value is the distance from zero on the number line). Of course, this mean that all complex numbers on a circle with the same radius centered at the origin have the same absolute size.

(so, to answer my own question, |i| = |1| = |-1| = |-i|).