Answer all odd-numbered problems.

Find x and y so that the statements in Probs. 49 to 56 Problems 65 to 68 deal with some of the field proper are true. Use the definition that ties of the complex numbers. at bi =c + di if and only if a = c and b = d 65. As an example of the associative law of multiplica- 49. x + 2/ + 2 = 5 + yi 50. x - 5i = 4 + 2i - yi tion, calculate both 51. y + ix - 3/ = 2+ 3/ 52. 5+x+i= 2+ yi (1 - 27)(3 + 1) . (5 + 31) 53. (x + iy)(1 + 37) = -1 + 7/ 54. (x - 2/y)(3 + i) = 20 and (1 - 21) . (3 + 1)(5 + 31) 55. (x - iy)(3 - 50) = -6 - 241 and show that they have the same value. 56. (x - iy)(2 + 37) = 4 + 6i 57. Show that the value of x2 - 10x + 29 is 0 if x = 66. As an example of the commutative law of multipli- 5+ 2i. cation, calculate both 58. Show that the value of x3 + 14x + 58 is 0 if x = (3 - 47) . (6 + 51) and (6 + 57) . (3 - 41) -7+ 31. 59. Show that the value of x2 - 12x + 37 is 0 if x = and show that they have the same value. 6- i. 67. As an example of the distributive law, calculate both 60. Show that the value of x2 - 16x + 289 is 0 if i'= 8 + 15i. (4 - 31) . [(6 + 71) + (-2 + D)] 61. Let z = (-1.+ /V3)/2. Show that and (4 - 31) . (6 + 71) + (4 - 31) . (-2 + 1) =1 and 1+z+2 =0 and show that they have the same value. 62. Let w = (-1 - iV3)/2. Show that 68. If a + bi = 0, show that the multiplicative inverse of a + bi is a - bi and Itwt w =0 02+ 62 by calculating that 63. Let z = (1 + 1)/V2 and show that (a + bi) a - bi = - a2 + 62 = 1