# TWSB: C is for Complex Number, That’s Good Enough for Me

Well this is one of the coolest things I’ve ever learned about.

So I’m in Complex Variables this semester, right? Today we talked about how to take limits of complex numbers as well as the closely related topic of infinity.
I’m assuming most people who read this regularly (or just happen to stumble upon it) know at least a little about infinity in the context of real numbers. Mainly, if we represent the reals on a number line, we have a direction that goes off towards negative infinity and a direction that goes off to positive infinity. But does this translate to complex numbers?

Well, not really. When we deal with complex numbers, we deal with the complex plane: a 2-D space with one axis representing the real part of a number and the other axis representing the imaginary part of a number. That is, one way we can think of a complex number is as a set of coordinates on the complex plane. For example, if I had the number z = 3 + i2, I could represent it with the coordinates (3,2) and plot it like this: Since we’re now dealing with a plane, we actually have infinitely many directions that can be thought of as infinity—basically, any direction out from the origin.

So how do we define infinity in the complex plane to allow us to, among other things, take limits involving the point at infinity? 