Complex Numbers Test – Algebra 2 Math (Printable PDF)

Question 1 Place the numbers in the regions (2 points)

Each region letter in the figure names the smallest set that contains a number. Write the letter for each number.

1. 36/4
2. −√100
3. 0.125
4. √40
5. √(−16)

(2 points)

Question 2 Simplify negative square roots (2 points)

Simplify.

1. √(−150) (1 point)
2. −3 + √(−48) (1 point)

Question 3 Add and subtract (2 points)

Perform each operation.

1. (8 − 5i) + (−3 + 12i) (1 point)
2. (−6 + 9i) − (4 − i) (1 point)

Question 4 Multiply complex numbers (3 points)

Multiply and write each answer as a + bi.

1. (4 − 3i)(5 + 2i)
2. (6 − i)²
3. (7 + 2i)(7 − 2i)

Question 5 Powers of i (2 points)

Evaluate each power.

1. i⁴⁷ (1 point)
2. i⁸² (1 point)

Question 6 Two points on the complex plane (2 points)

The figure shows points P and Q.

1. Write P and Q as complex numbers. (1 point)
2. Find P + Q. (1 point)

Question 7 Solve for a and b (3 points)

Find real numbers a and b such that (a + 2b) + (3a − b)i = 11 + 5i.

Question 8 Verify a solution (2 points)

Show that 2 − 3i is a solution of x² − 4x + 13 = 0.

Question 9 Circuit calculations (2 points)

A series circuit has two parts with impedances 9 + 4i ohms and 5 − 7i ohms.

1. Find the total impedance. (1 point)
2. A current of 1 + 2i amps flows through a part with impedance 3 − 4i ohms. Find the voltage (current times impedance). (1 point)