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.

(7 - 5i)(- 2 - 3i)

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 in standard form And the multiplication that we're going to be doing is 3 -2 i times 1 -1. And whenever you're multiplying complex numbers it's very similar to multiplying polynomial. Where you want to make sure that each term in the first parentheses gets multiplied by each term in the second parentheses. So if I do that I have three times one is three then three times negative I is negative three. I and then I have the second term of the first parentheses negative two I times one. So negative two I. And negative two I times negative I so positive to I squared. So now I've multiplied each term from the first set of parentheses to the second set of parentheses. And I can combine these middle terms. So I'm left with 3 -5 I plus two I squared. And whenever you're dealing with complex numbers it's also important to remember that I is equal to the square root of negative one. So I squared is equal to negative one. So you can see that negative one is a real No. So whenever I get squared it becomes real. So I'm gonna go back to my expression and wherever I see an I squared I'm going to replace it with the -1. So I have three minus five. I plus two and replacing the I squared with negative one. So now if I carry out this multiplication I have 3 - I -2, and I can combine the three and the two to leave me with 1 - I. And you can see that this is written in standard form because we have the real part first, A plus B. I, and the imaginary part second. So this becomes my final answer and one minus five I aligns with answer choice D. So hopefully this video helped and see you next time.

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