Question: Solve all the odd-numbered problems. Perform the indicated operations in Probs. 1 to 32. Verify the fact that (z)? = zZ in each of Probs.

Solve all the odd-numbered problems.

Perform the indicated operations in Probs. 1 to 32. Verify the fact that (z)? = zZ in each of Probs. 33 to 36 1. (2 + 37) + (7 + 21) 2. (5 + 40) + (4 + 37) 33. 3 + 5i 34. 5 - 2i 3. (3 - 21) - (4+ 1) 4.- (3 - 60) - (2-31) 35. : 1 - 71 36. 4 + 3i 5. (3 - 41) - (4 - 31) 6. (9 + 50) - (-4+ 30) 7. (-5 - 81) - (6 -91) 8. (6-51) + (5 -61) Prove the statement in each of Probs. 37 to 40 for 9. (3 + 27)(3 - 41) 10. (4 - 50)(2 + 90) 11. (3 - 27)(3 + 21) and w=c + di 12. (4 + 50)(4 + 51) = =at bi 13. (4 - 60(3 + 71) 14. (7 + 60)(6 - 71) 37. IFW =I+w 38. 7- W = 1-W 15. (3 - 71)(3 - 51) 16. (7- 51)(5 + 71) 39. = iW 40. z + 7 is real 2 - 31 17. 1 - 81 18. 4+ 5i 8+1 For any two complex numbers z = a + bi and w = 4 - 51 c + di, the triangle inequality holds. 19. 5 - 31 20. 7 - 61 5 + 2i 12 + w/ s /2) + /ml 21. 4+7i 13i 4 - 71 22. 3+ 2/ Verify this in the specific cases in Probs. 41 to 44. 23. 14 + 481 14 - 48i 41. z = 3 + 5i, w = 6 - 4i 7 - i 24. 42. z = 18 + 7/, w = -ll+ i 7+1 43. z = 6+ 5i, w= -12 - 107 25. 2+ 3i 4 - 31 4+1 4- 1 + 2-31 4+ 31 26. 44. 1= -8 + 3i, w = 4 - 9/ 4 - 31 4+ 37 27. 3 + 41 3 - 4i 3+ 2i 1 + 51 2-1 + Verify the statements in Probs. 45 to 48, where n is 28. 2+1 1 + 5i 3+ 21 any positive integer. 29. 14 + 3/ 30. 13 - 41 45. imPuPapepsi 31. 1-5 + 121 46

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