In Exercises 9–20, find each product and write the result in standard form. (3 + 5i)(3 − 5i)

Welcome back, everyone. Calculate the product of two minus three I and two plus three I and express your answer in standard form where given for answer choices A says negative 13 B 13 C five plus six, I and D five minus six, I. So we're looking at the product of the two conjugates. Essentially, we begin with two minus three I and we have to multiply that by two plus three I, we can essentially use the foil method or we can notice that this is in a form of A minus B multiplied by A plus B which is the reverse of the factorization of the difference of squares, right? We have a squared minus B squared. So in this case, our A is two and our B is three I. So when we expand this, we're going to get two squared minus we I squared. Now let's simplify T squared is four and then we are subtracting nine I squared. Let's recall that I squared is equal to negative one. So we get four minus nine multiplied by negative one which is four plus nine and that's 13. So we can conclude that the correct answer to this problem is option B, thank you for watching.