Bluebook SAT Test Complex Numbers

Question 1

What is the value of i²?

Accepted Answer

-1

Answer

By definition, i is the imaginary unit where i² = -1.

Question 2

What is the sum (3 + 2i) + (4 − 5i)?

Accepted Answer

7 − 3i

Answer

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)?

Accepted Answer

5 + i

Answer

Expanding: 2 − 2i + 3i − 3i² = 2 + i − 3(−1) = 2 + i + 3 = 5 + i.

Question 4

What is the complex conjugate of (4 − 7i)?

Accepted Answer

4 + 7i

Answer

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?

Accepted Answer

−i

Answer

i³ = i² × i = (−1)(i) = −i.

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