Hey, everyone now that we know what complex numbers are, we can perform operations on them like addition and subtraction. Now I know you may be thinking that this is just yet another new skill you're going to have to learn. But adding and subtracting complex numbers is actually exactly the same as adding and subtracting algebraic expressions. So we're just going to take a skill that we already know and apply it to our complex numbers. Let's go ahead and jump in. So just like with algebraic expressions, when you add and subtract complex numbers, you're just going to combine like terms. So when I'm given algebraic expressions to add, let's say four plus eight X plus two plus three X, then I just need to remove my parentheses and then combine any like terms I have. So here I have four and two, both constants that combine to six and then I have eight X and three X, both X terms that combine to 11 X. So when I'm working with algebraic expressions, I have some constants and some terms with variables that get combined to give me my final solution. When I'm working with complex numbers, I still have constants. But instead of terms with a variable, I have terms with an I with my imaginary unit. So I'm really just gonna treat that I as though it is a variable. So let's look at adding these complex numbers. So here I have four plus eight, I plus two plus three, I, so let's go ahead and get rid of all of those parentheses. So I have four plus eight, I plus two plus three. I and now I can just combine like terms. So I have constants four and two, which are gonna combine to give me six and then I have my imaginary terms. Eight I and positive three I which are gonna combine to give me positive 11. I. Now one thing that we need to consider whenever we're adding or subtracting complex numbers is that we always want to express our final answer in standard form. Now remember standard form for complex numbers is just A plus B I. So I got six plus 11 I here, which is already in that standard form. So my final answer is six plus 11. I let's take a look at subtracting some complex numbers. So again, I have four plus eight, I, but now minus two plus three. I, so let's go ahead and remove those parentheses. So I have four plus eight, I, but now since I'm subtracting, I need to make sure that I distribute that negative into my parentheses here. So I'm left with a minus two now and a minus three, I now I can simply combine like terms as I did before. So again, my constants four and then negative two, these will combine to give me a positive two and then I have A I and negative three. I, so my A I and negative three, I are gonna combine to give me a positive five. I, now again, we want to make sure that our answer is in standard form here A plus B I and it is. So my final answer is two plus five I and that's all there is to adding and subtracting complex numbers. I'll see you in the next video.