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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. What is (3 + 2i) − (1 − 4i)?

    Answer: 2 + 6i

    Subtract real parts (3 − 1 = 2) and imaginary parts (2 − (−4) = 6) to get 2 + 6i.

  2. Which of the following equals i^17?

    Answer: i

    Since i cycles with period 4, 17 = 4 × 4 + 1, so i^17 = i^1 = i.

  3. What is (1 + i) ÷ (1 − i)?

    Answer: i

    Multiplying numerator and denominator by (1 + i): (1 + i)² / ((1)² + (1)²) = (1 + 2i − 1)/2 = 2i/2 = i.

  4. If z = 3 − 4i, what is the product z × z̄ (where z̄ is the complex conjugate of z)?

    Answer: 25

    (3 − 4i)(3 + 4i) = 9 − (4i)² = 9 − (−16) = 25, which is always a real number.

  5. What is the real part of the product (5 + 3i)(2 − i)?

    Answer: 13

    (5 + 3i)(2 − i) = 10 − 5i + 6i − 3i² = 10 + i + 3 = 13 + i, so the real part is 13.

  6. What is the value of (2i)³?

    Answer: −8i

    (2i)³ = 8i³ = 8(i² × i) = 8(−1)(i) = −8i.

  7. What is (6 + 4i) ÷ 2?

    Answer: 3 + 2i

    Divide both the real and imaginary parts by 2: (6/2) + (4/2)i = 3 + 2i.