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Liberty University
Adding Subtracting And Multiplying Complex Numbers - Example 4


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this set of complex numbers. And here we have three sets of complex numbers. We're gonna multiply now. We're going to use the foil method to do so. But what's gonna happen is because we're multiplying. Three different polynomial is with, um, we're actually going to kind of do this full method twice. So the first time we're gonna do the full method, we're gonna do it with our first two parentheses. So we'll hold on the four plus three, I we're gonna use it. And after we find their solution, So let's do our foil. So we have negative five times six for the outside would be negative five times negative. I the inside would be too, I time six. And our last numbers would be two i times negative. I that would be 30 and then we'd have five I and we'd have 12 I and then we would have negative, too. I squared and remember that I squared equals negative one. So what we would have is would have negative two times negative one, which would be positive too. So what we would have is 30 plus five I plus 12 I plus two. So that means combine like terms that have 32 plus 17 I. So that's the solution to the first two. So now that we have that, let's move on and let's multiply that times our last one. I apologize. That's supposed to be negative. 30. So that would actually be negative. 28 because that's a negative five. I miss my that. All right, so we have negative. 28 plus 17 I times four plus three I. So now we'll do a little method again to multiply these. So we have front outside inside. Last our first one's or negative four. I'm sorry. Number 28 times. Four Outside or negative. 28. Tom's three I inside. It's 17 items four and our last is 17 I times three I so that's gonna be negative. 28 times four is negative. 112 negative. 28 times three is negative. 84 I 17 times four. It's 68 I, and 17 times three is 51 items eyes I squared, which we know I squared equals negative one. So that's gonna actually be 51 times negative one, which is negative. 51. So now that we've got that Let's combine like terms. So we have negative 112 minus 84 I plus 68 I minus 51. So when I combine like terms, that's gonna give me negative. 163 minus 16 I So my final solution is negative. 1 63 minus 16.