Explanation for Question 18 From the Math (No Calc) Section on the 2018 April Sat
Question 18 asks in the complex number system. 2 What is the value of the expression? 16. 3 I, to the fourth minus eight, I squared plus four and it tells 4 us that I is equal to root negative one. 5 So I'm going to start by finding the values of I squared and I 6 to the fourth. So I know that I as equal to root negative one, 7 which means that I squared is equal to root negative one times root 8 negative one, which is just equal to negative one. 9 And then if I square that to get I to the fourth negative 10 one times negative one is just equal to positive one. 11 So now I know that I squared is equal to negative one and I 12 to the fourth is equal to positive one. 13 So I can plug that into our problem. So I have 16 times I 14 to the fourth, which is times one minus 15 eight times, 16 negative one plus four. 17 So this is 16 plus a plus 18 four. And when I do that, 19 I get 28. So I know that the answer to this question 20 is 28.