In Exercises 9–20, find each product and write the result in stan...

Question

In Exercises 9–20, find each product and write the result in standard form.

(- 5 + 4i)(3 + i)

Accepted Answer

Hello everyone in this video we're going to be working on this practice problem that deals with complex numbers and we want to make sure that our answer is written in standard form and the multiplication that we're going to be doing is seven plus two I times I minus five. So when you're multiplying complex numbers, it's very similar to multiplying polynomial. Where you want to make sure that each term in the first set of parentheses gets multiplied to each term in the second set of parentheses. So if we do that we have seven times I is seven I seven times negative five is negative 35 I times I is to I squared and two I times negative five is negative 10. I So you can see that we can combine the first and the last term. So we're left with negative three, I minus 35 plus two I squared. And another important thing to remember when you're working with complex numbers is that I represents the square root of negative one. So if we have I squared, that's the same thing as negative one. So you can see that when you square the eye it becomes a real number Since it becomes -1. So now I'm going to go back to this expression that we've written and wherever I see an I squared I'm going to substitute in the negative one or replace it by negative one. So this becomes negative three, I minus 35 plus two times negative one. And if I do that multiplication, I'm left with -3, I -35 -2. So this becomes -3 I -37. And remember that we want our answer in standard form where we have the real part plus the imaginary part. So I'm gonna rewrite my answer in standard form So I have negative 37 -3 I and this becomes my final answer and you can see that this aligns with answer choice D. So hopefully this video helped and see you next time.

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