466 ALGEBRAIC SYSTEMS [APP. B
B.60. f( 1 )=0,f(i)=1,f(− 1 )=2,f(−i)= 3
B.62. (a) {(0, 0)}, (b){ 2 πr|r∈Z}.
B.69. (a) 1, 5, 7, 11; (b) 4, 10; (c) {2, 10}.
B.70. (a) 28, 23, 19; (b) 13, 11, 26−^1 does not exist since
26 is not a unit.
B.72. Show −a = a using a +a = (a+a)^2.
Then showab=−baby(a+b)=(a+b)^2.
B.73. (b)− 1 = 0 −element, 0= 1 −element.B.91. Showfis an isomorphism wheref([
a −b
ba])
=
a+bi.
B.93. Hint: Use Problem B.92.
B.95. (a) −1, ( 3 ±√
21 )/2; (b) −2, ( 3 ±√
29 )/2;
(c) 3,(− 5 ±√
17 )/ 2
B.96. (a)− 1 /2, 1± 2√
2; (b) 3/2,(− 1 ±√
13 )/ 2
B.97. 2 ±3i,( 1 ±√
5 )/ 2
B.98. 1 ±i,(− 1 ±√
21 )/ 2