Consider II. What do you think of when you see (y + x)(y – x)? This expression is another way of
writing the classic factorable y^2 – x^2 . So y^2 – x^2 > 0, which means that y^2 > x^2 . If x ≤ y, “could it be true”
that y^2 > x^2 ? Sure—as Picking Numbers shows: Say x = 1 and y = 2. So II must also be included in the
answer, which must be (D).
Only for the sake of rounding out your knowledge, consider III. If x ≤ y, “could it be true” that x – y >
0? If x – y > 0, then x > y. If x ≤ y, it could not be true that x > y.
The answer is (D).
IMAGINARY AND COMPLEX NUMBERS
There’s a chance you will encounter a question that begins, “If i^2 = –1...,” like the example below.
Example 2RULES OF IMAGINARY NUMBERS
1. If , then which of the following has the greatest value?(A) i^4 + i^3 + i^2 + i(B) i^8 + i^6 + i^4 + i^2(C) i^12 + i^9 + i^6 + i^3(D) i^16 + i^12 + i^8 + i^4(E) i^20 + i^15 + i^10 + i^5