University:
Missouri State University
Course:
MTH 103 | Intermediate Algebra
Academic year:

2019
Views:

234

Pages:

3
Author:

jbroieduroseba4

6-8 NAME DATE Practice Worksheet Imaginary Numbers Simplify. 1. sqrt(- 49) * Fi 2. sqrt(- 48) * 4sqrt(3) * i 3. 6sqrt(- 12) * 12sqrt(3i) 4. sqrt(- 16/25) * 4/5 * j sqrt(- 2/7) * (sqrt(14))/7 * i 6. sqrt(- 8/3) * (2sqrt(6))/3 * i 7. i ^ n - 1 8. 9. i ^ m * L ^ c 10. 6 1 11. sqrt(- 8) * sqrt(- 18) - 12 12. sqrt(- 42) * sqrt(- 6) - 6sqrt(7) 13. (5sqrt(- 6))(3sqrt(- 10)) - 30sqrt(15) 14. (2sqrt(- 3))(- 5sqrt(- 27)) 90 15. (sqrt(- 7)) ^ 4 * 49 ^ 11 16. (sqrt(- 5)) ^ 3 - 5sqrt(5) * i 17. 3i * (4i) ^ 2 - 48 * i deg 18. (- 5i) ^ 2 * (6i) - 150i Solve each equation. 19. n ^ 2 + 25 = 0 plus/minus 5 * i ^ (1/2) 20. m ^ 2 + 10 = 0 plus/minus sqrt(10) * i 21. tit 6y ^ 2 + 42 = 0 22. 4r ^ 2 + 64 = 0 plus/minus 4 * i 23. v ^ 2 = - 81 plus/minus 9 * i 24. 5x ^ 2 = - 125 plus/minus 5 * i 6-9 NAME DATE Practice Worksheet Complex Numbers Simplify. 1. (7 - 6i) + (9 + 11i) 16 + 5i 2. (5 + sqrt(- 8)) + (- 13 + 4sqrt(- 2)) - 8 + 6sqrt(2) * i 3. (- 5 + 2i * sqrt(7)) rightleftharpoons(2-7i sqrt 7 ) - 7 + 9i * sqrt(7) 4. (- 3 - 10i) - (- 5 - 4i) 2 - 6i 5. - 6(2 - 8i) + 3(5 + 7i) 3 + 69i 4(7 - i) - 5(2 - 6i) 18 + 26i 7. (3 + 5i)(4 - i) 17 + 17i 8. (4 - 2i * sqrt(3))(1 + 5i * sqrt(3)) 34 + 18i * sqrt(3) 9. (3 - 4i) ^ z - 7 - 24j 10. (sqrt(5) + 2i) ^ 2 1 + 4i * sqrt(5) 11. (6 - 4i)(6 + 4i) 52 12. (8 - sqrt(- 11))(8 + sqrt(- 11)) 75 13. 5(2 + 3i) + 6(8 - 5i) 58 - 15i 14. 7(2 + 6i) - 9(- 3 + 4i) 41 + 6i 15. (3 - i)(1 + 2i)(2 + 3i) - 5 + 25i 16. (4 + 3i)(2 - 5i)(4 - 3i) 50-150i Find the values of x and y for which each equation is true. 17. 3x - 5yi = 15 - 20i x = 5 Y = 4 18. sqrt(3) * x + 7yi = 6 - 2i x = 2sqrt(3) y = - 2/7 19. (x - y) + (2x + y) * i = - 3 + 9i x = 2 y = 5 20. (2x - y) + (x + y) * i = - 4 - 5i x = - 3 y = - 2 6-10 NAME Practice Worksheet DATE Simplifying Expressions Containing Complex Numbers Simplify. (2 - 4i)/(1 + 3i) - 1 - i deg (3 - i)/(2 - i) * (7 + i)/5 (6 + 5i)/(- 2i) * (- 5 + 6i)/2 (1 + 6i)/(5i) * (6 - i)/5 (3 - 6i)/(- 4i) * (6 + 3i)/4 6. (2 + 7i)/(- 5i) * (- 7 + 2i)/5 3/6 + 4i 9-6i 26 8. 2/(7 - 8i) * (14 + 16i)/113 9. 3/(sqrt(2) - 5i) * (sqrt(2) + 5i)/9 10. (2 + i * sqrt(3))/(1 + i * sqrt(3)) * (5 - i * sqrt(3))/4 11. ((1 - 2i) ^ 2)/((2 - i) ^ 1) * (7 - 24i)/25 12. (2 + i)/((1 - i) ^ 2) * (- 1 + 2i)/2 13. 3/(sqrt(5) + 2i) * (sqrt(5) - 2i)/3 14. (2 - i)/(sqrt(2) + 2i) * (- 2 + 2sqrt(2) - (4 + sqrt(2)) * i)/6 15. ((1 + 3i) ^ 2)/((4 - i) ^ 2) * (- 168 + 26i)/289 16. (2 - i * sqrt(3))/(1 + i * sqrt(3)) * (- 1 - 3i * sqrt(3))/4 Find the multiplicative inverse of each complex number. 5 + 2i * (5 - 2i)/29 3 - i * (3 + i)/10 19. i/(7 + 4i) * 4 - 7i 20. -6i 4- overline 6i (5 + 4i)/6