Everyone. So not only can we add and subtract complex numbers, but we can also multiply them. Now, multiplication might seem a bit more intimidating than adding or subtracting. But we're actually still going to multiply our complex numbers the same way we multiply algebraic expressions. So we're again, gonna take a skill that we already know and apply it to our complex numbers. And don't worry, I'm still going to walk you through it step by step. So let's go ahead and take a look. Now, algebraic expressions are always multiplied one of two ways. So complex numbers will be the same, we either distribute or we use foil. Now, when we either distribute or foil, we're always going to end up with an I squared term. Now, we know that I squared is just equal to negative one. So I'm going to use that in order to simplify my final answer. So let's go ahead and just jump right into an example. Looking at my first expression over here, I have three I times seven minus two. I now my very first step is going to be to either distribute or foil and looking at my expression here I have this three I by itself. So since it's just one term of multiplying this other complex number, I'm going to go ahead and distribute. That seems like the best choice here. So I'm going to distribute this three I into my seven and my negative two I in order to get 21 I and then three I times negative two I is going to give me negative six I squared. Make sure when you're multiplying an I by an I I, you get I squared. So step number one is done and I can go ahead and move on to step two, which is to apply the fact that I squared equals negative one. So looking at my expression here of 21 I minus six I squared. So I have my I squared right here and I need to take this whole term and simplify it using I squared equals negative one. So this negative six I squared just becomes negative six times negative one and negative six times negative one is just positive six. So I can bring my 21 I down here and I have 21 I plus six. So I've completed step two and step three is to combine my like terms. Now looking over here, I don't have any like terms that need to get combined. So step three is also done. And this is my final answer, but I wanna make sure that I express my answer in standard form. So here at 21 I plus six and I know that standard form is A plus B I. So I'm gonna go ahead and flip this around in order to get six plus 21 I, and this is gonna be my final solution. So let's go ahead and look at another example. So over here I have negative six plus two, I times three plus four. I let's go ahead and start with step one, which is either to distribute or foil. Now, since I have two complex numbers that each have two terms in them, it looks like foiling is to be my best option for step one. So let's go ahead and foil. So I'm gonna start with my first terms. So negative six times three is gonna give me negative 18 and then I have my outside terms negative six times four, which is gonna give me or times four I which is gonna give me negative 24. I, then I have my inside terms two, I times three is gonna give me positive six I and then lastly my last terms which is two I times four. I now this since I'm multiplying two I terms, I'm gonna end up with an I squared. This is gonna give me plus eight I squared. OK. So we have completed step number one. Let's go ahead and move on to step two, which is to apply that I squared equals negative one. Now I definitely have an I squared term over here. I have this eight I squared. So I'm gonna go ahead and simplify this whole term into eight times negative one. Now, eight times negative one is just negative eight. So I have applied my I squared equals negative one and I can go ahead and pull all of my other terms down as well, so I can bring my negative 18 and then I have both of my I terms negative 24 I and positive six. I. So now step three is to combine all of my like terms and I have some like terms that need to get combined here. So negative 18 and negative eight are going to combine to negative 26. And then my other like terms are these I terms negative 24 and positive six I which are gonna combine to give me negative 18. I. So my final answer I've completed step three. I've combined my light terms. I have negative 26 minus 18. I and I of course want to check that this is in standard form A plus B I and it is so I'm good to go and this is my final answer. That's all for this video. I'll see you in the next one.