Bluebook SAT Test Complex Numbers 2 — Questions and Answers

Correct answer: 2 + 6i

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

Correct answer: i

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

Correct answer: i

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

Correct answer: 25

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

Correct answer: 13

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

Correct answer: −8i

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

Correct answer: 3 + 2i

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

Bluebook SAT Test Complex Numbers 2

What is (3 + 2i) − (1 − 4i)?

Select your answer