Question 1
Which of the following is equivalent to (1 + 3i)(1 - 6i), where i² = -1?
- A.
19 - 17i
- B.
19 - 3i
- C.
1 - 18i
- D.
-17 - 3i
Answer: B. 19 - 3i
Multiply using FOIL: (1)(1) + (1)(-6)i + (3)(1)i + (3)(-6)i² = 1 + (-3)i + (-18)(-1) = 19 - 3i.
ACT · Math · Preparing for Higher Math: Number and Quantity
Complex numbers
Complex numbers is part of Preparing for Higher Math: Number and Quantity in the ACT Math section. The questions below are written in the style of the real test, each with the answer and a worked explanation.
Question types you will see here include powers of i, add or subtract complex numbers, multiply complex numbers and divide using the conjugate.
Common traps: not reducing the exponent by multiples of 4; mixing up i cubed and i; treating i squared as 1.
Sample questions
Question 2
Which of the following is equivalent to (2 + 6i)(-6 - 4i), where i² = -1?
- A.
-12 - 24i
- B.
12 - 44i
- C.
12 - 36i
- D.
-36 - 44i
Answer: B. 12 - 44i
Multiply using FOIL: (2)(-6) + (2)(-4)i + (6)(-6)i + (6)(-4)i² = -12 + (-44)i + (-24)(-1) = 12 - 44i.
- A.
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