[Video] Q14: 8 - i/ 3-2i if the expression above is rewritten in the form a +bi, where a and b are real numbers, what is the value of a ? (note: i = sqrt(-1))

Explanation for Question 14 From the Math (No Calc) Section on the Official Sat Practice Test 4

So right now we have this expression here, 2 eight months, I over three minus two Y, and we're trying to get rid 3 of the fraction, essentially. We're trying to write it is just one expression, 4 a plus B I. And so some background knowledge that you need to know 5 is that in order to work with imaginary numbers to go from fraction and 6 no fraction is you need to multiply by what we call the conjugate. 7 And the conjugate is essentially, um, 8 just the denominator, but we change the sign in the denominator. 9 So here we have three minus two. 10 I, so our conjugate is three plus two. 11 I, so we're going to multiply the top and the bottom by three plus 12 two. I, so when we multiply that out, 13 you'll see that the bottom, or I guess rather the tough right now, 14 we'll start with the bottom three times three, 15 that gives us nine. 16 Then we have a plus two, I minus two. I, 17 so those cancel out or plastics, I minus six and then negative two times 18 positive two that's minus four times I squared. 19 So that is our denominator. And then we need to look at 20 what our top is going to be. Right? 21 So we have, um, eight times three that's 24. 22 Um, we have eight times positive two I, 23 that is going to be plus 16 I three times negative. 24 I that's minus three. I, and then we've got negative one times 25 positive two. I right. 26 That's negative two. 27 I squared. Okay. So there is a lot of multiplying there, 28 but the next step now is going to be to take everything that ...