## Complex Numbers

Complex numbers are kind of like binomials. They have two parts: a real number and an imaginary number. Some examples of complex numbers would be (3 + 4i) , (-2, -i), or (7 – 3i). Make sense? We’ve got the real and the imaginary working together in peace and harmony.

Let’s talk about what you can do with them.

## Addition and Subtraction

There are two ways to think about adding and subtracting complex numbers: the simple way and the smarty-pants-math way. We’ll take a quick look at both.

### The Simple Way

Combine like terms. Seriously, that’s it.

Okay, fine, we can do an example.

We’ll add our real numbers first, then the imaginary ones.

So our answer is 1 + 3i.

Simple, yeah? Let’s try subtraction. Watch out for the negative signs!

So our answer is -3 – 2i.

### The Smarty-Pants-Math Way

Who likes to memorize formulas? I hear lots of crickets chirping out there, but let’s look at it anyway.

You can think of a complex number as *a + bi. *In this case, the *a* and *b* can be substituted by any real number.

So, if you want to add two of them together, you get this:

Make sense? Combine *a *and *c* like we did in *The Simple Way,* then combine *b *and *d, *tacking the *i* on at the end.

Let’s look at subtraction.

Easy enough, right? These are all operations you should be really familiar with, so hopefully this was a piece of cake!