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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

  1. Which of the following is a solution to x² + 4 = 0?

    Answer: x = 2i

    x² = −4 gives x = ±√(−4) = ±2i, and 2i is one of the solutions.

  2. If (a + bi)(3 − 2i) = 12 + 5i, what is the value of a + b?

    Answer: 5

    Expanding gives (3a + 2b) + (−2a + 3b)i = 12 + 5i; solving 3a + 2b = 12 and −2a + 3b = 5 yields a = 2, b = 3, so a + b = 5.

  3. What is the modulus (absolute value) of the complex number 3 + 4i?

    Answer: 5

    |3 + 4i| = √(3² + 4²) = √(9 + 16) = √25 = 5.

  4. Which quadratic equation has solutions x = 2 + i and x = 2 − i?

    Answer: x² − 4x + 5 = 0

    (x − (2 + i))(x − (2 − i)) = (x − 2)² + 1 = x² − 4x + 4 + 1 = x² − 4x + 5 = 0.

  5. What is i^100?

    Answer: 1

    100 is divisible by 4 (100 = 4 × 25), so i^100 = (i⁴)^25 = 1^25 = 1.

  6. If z = a + bi and z + z̄ = 10, what is the value of a?

    Answer: 5

    z̄ = a − bi, so z + z̄ = 2a = 10, which gives a = 5.

  7. What is (3 − 2i) ÷ (3 + 2i)?

    Answer: 5/13 − 12i/13

    Multiply by (3 − 2i)/(3 − 2i): (3 − 2i)²/13 = (9 − 12i + 4i²)/13 = (9 − 12i − 4)/13 = (5 − 12i)/13.