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Name_________________________________ Date_________________ Alg2/Trig Complex Numbers Review 1. What is the sum of 2 4 and 3 16 expressed in a + bi form? (1) -1 + 2i (2) -1 + i 20 (3) -1 + 12i (4) -14 + i 2. The expression i 0 i 1 i 2 i 3 i 4 is equal to (1) 1 (2) -1 (3) i (4) -i 3. If f (x ) x 3 2x 2 , then f i is equivalent to (1) -2 + i 4. The expression (1) 1 (2) -2 – i i15 is equivalent to i3 (2) i (3) 2+ i (3) -1 (4) 2 – i (4) -i 5. If a and b are real numbers, then the product of a bi and a bi is (1) (2) (3) (4) always imaginary always a real number sometimes, but not always, a real number sometimes, but not always, imaginary 6. Which of the following is the additive inverse of -4 + 7i? (1) -4 – 7i (2) 4 + 7i (3) 4 7 i 65 65 (4) 4 – 7i 7. Express the roots of the equation 4x 2 32 0 in simplest a + bi form. 8. Express the multiplicative inverse of 6 – 4i in simplest a + bi form. 9. Multiply. Put your answer in simplest a + bi form. a.) 1 i 2 2 i 2 b.) 1 5i 2 i 10. Simplify each of the following. Put all answers in simplest a + bi form. Show all work. a. 6 8i 3i b. 2 i 3i c. 108 2 11. Simplify: (2 i 3)2 13. Simplify: 12. Simplify: 5 1 i 7 i 4 4 2 5i 3i 5 3 4i 14. Solve for x and y: 3 x 4yi 10 i 15. Graph and label the complex number u = 2 – 4i and v = -4 – 5i. Then graph and label u + v. ANSWERS 1. (1) 2. (2) 3. (4) 4. (1) 5. (2) 6. (4) 7. x 2i 2 8. 3 1 i 26 13 9a. 4 i 2 9b. 7 – 9i 10a. 8 2i 3 10b. 1 1 i 2 2 10c. 3i 6 11. 1 4i 3 12. 1 117 i 2 16 13. -6 + 2i 14. x 7, y 1 4