[Video] Q4: Which of the following complex numbers is equal to (5+12i) - (9i^2 -6i), for i = sqrt(-1)

Explanation for Question 4 From the Math (No Calc) Section on the Official Sat Practice Test 7

Question four asks, which of the following complex numbers is equal to five 2 plus 12. I minus nine, 3 I squared minus six. 4 I for I is equal to root negative one. 5 So the first thing that we're going to do here is add and subtract 6 like terms. So I'm going to rewrite this as 12. 7 I plus negative nine I squared 8 or I'm sorry. Wait, let me rewrite that. I'm going to rewrite this as 9 negative nine. I squared plus 10 12, I plus six plus 11 five. And the reason I did that was just to see the life terms 12 next to each other. So then I can add and subtract like terms and 13 this becomes negative nine. I squared plus 18. 14 I plus five. 15 Now the next thing I can do is I can actually substitute in a 16 number for I squared. And the reason I can do that is because we 17 know that I is equal to root negative one, 18 which means that I squared is equal to root negative one squared, 19 which is just equal to negative one. So we can actually substitute in negative 20 one for I squared here. So that gives us negative nine times negative one, 21 which is just positive nine plus five plus 18. 22 I, which simplified is 18. 23 I plus 14. 24 And that tells us that D is the correct answer.