C H A P T E R 2 Polynomial and Rational Functions
C H A P T E R 2 Polynomial and Rational Functions
C H A P T E R 2 Polynomial and Rational Functions
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74. 4.5x2 3x 12 0; a 4.5, b 3, c 12 75. 6i 3 i 2 6i2i i2 x 3 ± 32 44.512<br />
24.5<br />
<br />
3 ± 207<br />
9<br />
<br />
3 ± 3i23<br />
9<br />
1 23<br />
±<br />
3 3 i<br />
76. 4i 2 2i 3 4 2i 77.<br />
79.<br />
75 3 53i 3<br />
5 3 3 3 i 3<br />
12533 1i<br />
3753i<br />
81. 1 1 1 i<br />
<br />
i3 <br />
i i i<br />
83. (a)<br />
(b)<br />
84. (a)<br />
(b)<br />
(c)<br />
z 1 9 16i, z 2 20 10i<br />
1 1<br />
<br />
z z1 1<br />
z2 2 3 8<br />
<br />
511i 5i<br />
i i<br />
i 82.<br />
i2 1<br />
1<br />
9 16i <br />
1<br />
20 10i<br />
z 340 230i 29 6i<br />
29 6i 29 6i<br />
1 3i 3 1 3 31 2 3i 313i 2 3i 3<br />
1 33i 9i 2 33i 3<br />
1 33i 9 33i<br />
8<br />
1 33i 9i 2 33i 3<br />
1 33 i 9 33i<br />
8<br />
Section 2.4 Complex Numbers 185<br />
61i 1<br />
6i 1<br />
1 6i<br />
5i 5 5i 2 i 2 i 78. i 3 1i 3 1i i<br />
80. 2 6 2i 6 8i 6 8i 4 i 2 8<br />
1<br />
2i<br />
1 1<br />
3 8i 3 8i<br />
1 3i 3 1 3 31 2 3i 313i 2 3i 3<br />
85. (a)<br />
(b)<br />
(c) 2i4 24i 4 2<br />
161 16<br />
4 2<br />
16<br />
4 16<br />
(d) 2i 4 2 4 i 4 161 16<br />
<br />
20 10i 9 16i<br />
9 16i20 10i<br />
11,240 4630i<br />
877<br />
11,240<br />
877<br />
<br />
4630<br />
877 i<br />
86. (a)<br />
87. False, if b 0 then a bi a bi a.<br />
88. True<br />
That is, if the complex number is real, the number equals<br />
its conjugate.<br />
29 6i<br />
340 230i<br />
(b)<br />
i 40 i 4 10 1 10 1<br />
i 25 i 4 6 i 1 6 i i<br />
8i 8i 1<br />
<br />
8i 64i 2 8 i<br />
(c) i50 i 412i 2 11 1<br />
(d) i 67 i 4 16 i 3 1i i<br />
i6 4<br />
i6 2<br />
x 4 x 2 14 56<br />
14 ? 56<br />
36 6 14 ? 56<br />
56 56
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