Complex Numbers Flashcards
7 cards from real Bluebook SAT Test practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 7 Complex Numbers flashcards as text
What is the value of i²?
Answer: -1
By definition, i is the imaginary unit where i² = -1.
What is the sum (3 + 2i) + (4 − 5i)?
Answer: 7 − 3i
Add real parts (3 + 4 = 7) and imaginary parts (2 − 5 = −3) separately to get 7 − 3i.
What is the product (2 + 3i)(1 − i)?
Answer: 5 + i
Expanding: 2 − 2i + 3i − 3i² = 2 + i − 3(−1) = 2 + i + 3 = 5 + i.
What is the complex conjugate of (4 − 7i)?
Answer: 4 + 7i
The complex conjugate of (a + bi) is (a − bi), so the conjugate of (4 − 7i) is (4 + 7i).
Which of the following is equal to i³?
Answer: −i
i³ = i² × i = (−1)(i) = −i.
What is (2 + i)²?
Answer: 3 + 4i
(2 + i)² = 4 + 4i + i² = 4 + 4i − 1 = 3 + 4i.
What is the value of i⁴?
Answer: 1
i⁴ = (i²)² = (−1)² = 1.