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Chapter 2 Polynomial and Rational Functions −14 + −12 −14 + i 12 = 2 2 −14 + 2i 3 = 2 −14 2i 3 = + 2 2
c.
Section 2.1 Check Point Exercises 1.
a.
(5 − 2i) + (3 + 3i) = 5 − 2i + 3 + 3i
= −7 + i 3
= (5 + 3) + (−2 + 3)i = 8+i b.
(2 + 6i) − (12 − i) = 2 + 6i − 12 + i
5.
2
−b ± b − 4ac x= 2a
= (2 −12) + (6 + 1)i = −10 + 7i
2.
a.
x2 − 2x + 2 = 0 a = 1, b = −2, c = 2
7i(2 − 9i) = 7i(2) − 7i(9i) = 14i − 63i 2 = 14i − 63(−1) = 63 + 14i
x=
−(−2) ± (−2) 2 − 4(1)(2) 2(1)
x=
2± 4 −8 2
2 ± −4 2 2 ± 2i x= 2 x = 1± i The solution set is {1 + i, 1 − i}. x=
b.
3.
(5 + 4i)(6 − 7i) = 30 − 35i + 24i − 28i 2 = 30 − 35i + 24i − 28(−1) = 30 + 28 − 35i + 24i = 58 −11i
5 + 4i 5 + 4i 4 + i = ⋅ 4−i 4−i 4+i = = =
20 + 5i + 16i + 4i 2
Concept and Vocabulary Check 2.1
16 + 4i − 4i − i 2 20 + 21i − 4
1.
16 + 1 16 + 21i
2.
17
1; 1 complex; imaginary; real =
16
+
21
i