So we've worked with real numbers like 3 and imaginary numbers like 2i separately, but you're often going to see expressions that have these two numbers together, so something like 3+2i. And these are actually called complex numbers when you have both a real number and an imaginary number added together. Now, complex numbers are going to be really important for us throughout this course and have a ton of different uses. And while they might sound a little complicated at first, I'm going to walk you through what they are and how we use them step by step. So let's get started. So a complex number has a standard form of a+bi. So in this complex number, a+bi, a is called the real part of the number, and b is called the imaginary part because it's multiplying i, our imaginary unit. Now it's important to know that b by itself is the imaginary part. It's not the whole term bi. So when I'm identifying the real and the imaginary part of the number I have up here, this 3+2i, 3 is going to be the real part of my number. And then 2 is going to be the imaginary part, just the 2 by itself.

Now, let's look at a couple of different examples of complex numbers and identify the real and imaginary parts of each of them. So first, I have this 4 − 3i. So looking at this number, the real part, a, is going to be this 4 because it's out there by itself. It's not multiplying my imaginary unit. This is going to be my real part, a. Then b, so I want to look for what is multiplying i, my imaginary unit. And in this case, it is negative 3. Now it's important to look at everything that's multiplying our imaginary unit. So if it's a negative number, if it's a square root, if it's a combination of a number and a square root, I want to get everything that's multiplying my imaginary unit. So in this case, b is going to be a negative 3. That's what's multiplying my imaginary unit i.

Let's look at another example. So here I have 0+7i. Now if I look for the real part of my number, what is not multiplying my imaginary unit, I have this as 0. So that means that, a, my real part is going to be 0. Then, b, my imaginary part, the part that's multiplying my imaginary unit i, in this case is going to be positive 7. Now you might look at this number and think, couldn't you just write that number as 7i? That zero isn't really doing anything. And you're right. I could just write this as 7i. But we still need to know that if we're looking at this as a complex number, it still has a real part. It's just 0.

So let's look at another example. So I have 2+0i over here. So what do you think the real part of this number is? Well, since this 2 is out here by itself, it's not multiplying my imaginary unit. 2 is going to be the real part of my number, a. Then looking at b, so the imaginary part, the part that is multiplying my imaginary unit, in this case, is just 0. So, again, you might be looking at this number thinking, isn't that just a real number? Couldn't I just write this as 2? And you're right. Again, I could just write this as 2. But remember, if we're looking at this as a complex number, it still has an imaginary part. It's just 0.

So that's all for this one, and I'll see you in the next video.