College Algebra 9th txtbk

82 CHAPTER 1 EQUATIONS AND INEQUALITIES
MATCHED PROBLEM 7
(A) Solve for real numbers x and y:
(2y 7) (3x 4)i 1 i
(B) Solve for complex number z:
(1 3i)z 4 5i 3 2i
The truth is that the numbers we studied in this section weren’t received very well when
they were invented, as you can guess from the names they were given: complex and imaginary.
These names are not exactly ringing endorsements.
Still, complex numbers eventually came into widespread use in areas like electrical
engineering, physics, chemistry, statistics, and aeronautical engineering. Our first application
of complex numbers will be in solving second-degree equations in Section 1-5.
ANSWERS TO MATCHED PROBLEMS
1. (A) Real part: 6; imaginary part: 7i; conjugate: 6 7i (B) Real part: 3;
imaginary part: 8i; conjugate: 3 8i (C) Real part: 0; imaginary part: 4i;
conjugate: 4i (D) Real part: 9; imaginary part: 0; conjugate: 9
2. (A) 9 2i (B) 7 5i (C) 2 2i (D) 0
3. (A) 26 7i (B) 6 18i (C) 3 2i (D) 13
1
4. (A) 5 10i
1 (B) 1 4i 5. (A) 0 (B) 1 3 4 3i
3
6. (A) 4i (B) 5 i17 (C) 5 (D) 13 13i
2 2 (122)i
7. (A) x 1, y 4 (B) z 2 i
1-4 Exercises
1. Do negative real numbers have square roots? Explain.
2. Arrange the following sets of numbers so that each one contains
the one that comes before it in the list: rational numbers,
complex numbers, integers, real numbers, natural numbers.
3. Is it possible to square an imaginary number and get a real
number? Explain.
4. What is the conjugate of a complex number? How do we use
conjugates?
5. Which statement is false, and which is true? Justify your
response.
(A) Every real number is a complex number.
(B) Every complex number is a real number.
6. Is it possible to add a real number and an imaginary number? If
so, what kind of number is the result?
For each number in Problems 7–18, find the (A) real part,
(B) imaginary part, and (C) conjugate.
10. 4.2 9.7i 11. 6.5 2.1i 12.
13. i
14. 6
15. 4
16. 2i 17. 5 i12 18. 4 i17
In Problems 19–44, perform the indicated operations and
write each answer in standard form.
19. (3 5i) (2 4i) 20. (4 i) (5 3i)
21. (8 3i) (5 6i) 22. (1 2i) (4 7i)
23. (9 5i) (6 2i) 24. (3 7i) (2 5i)
25. (3 4i) (5 6i) 26. (4 2i) (1 i)
27. 2 (3i 5) 28. (2i 7) 4i
29. (2i)(4i) 30. (3i)(5i) 31. 2i(4 6i)
3
5 4 5 i
32. (4i)(2 3i) 33. (1 2i)(3 4i)
34. (2 i)(5 6i) 35. (3 i)(4 i)
7. 2 9i 8. 6i 4 9. 3 2 5 6 i