Bluebook SAT Test Complex Numbers 1 — Questions and Answers
Question 1: What is the value of i²?
- 1
- -1 (Correct answer)
- i
- -i
Correct answer: -1
By definition, i is the imaginary unit where i² = -1.
Question 2: What is the sum (3 + 2i) + (4 − 5i)?
- 7 + 7i
- 7 − 3i (Correct answer)
- −1 + 7i
- 7 − 7i
Correct answer: 7 − 3i
Add real parts (3 + 4 = 7) and imaginary parts (2 − 5 = −3) separately to get 7 − 3i.
Question 3: What is the product (2 + 3i)(1 − i)?
- 5 + i (Correct answer)
- 5 − i
- −1 + 5i
- 2 + 3i
Correct answer: 5 + i
Expanding: 2 − 2i + 3i − 3i² = 2 + i − 3(−1) = 2 + i + 3 = 5 + i.
Question 4: What is the complex conjugate of (4 − 7i)?
- 4 + 7i (Correct answer)
- −4 + 7i
- −4 − 7i
- 7 − 4i
Correct answer: 4 + 7i
The complex conjugate of (a + bi) is (a − bi), so the conjugate of (4 − 7i) is (4 + 7i).
Question 5: Which of the following is equal to i³?
- 1
- −1
- i
- −i (Correct answer)
Correct answer: −i
i³ = i² × i = (−1)(i) = −i.
Question 6: What is (2 + i)²?
- 3 + 4i (Correct answer)
- 5 + 4i
- 4 + 4i
- 3 − 4i
Correct answer: 3 + 4i
(2 + i)² = 4 + 4i + i² = 4 + 4i − 1 = 3 + 4i.
Question 7: What is the value of i⁴?
- −1
- 1 (Correct answer)
- −i
- i
Correct answer: 1
i⁴ = (i²)² = (−1)² = 1.
Bluebook SAT Test Complex Numbers 1
What is the value of i²?