Practice C - MathnMind

ANSWERS
A48
Lesson 4.6, continued
Review for Mastery
1. 6i 2. 62i Ï }
3 3. 63i Ï }
2 4. 27 2 3i; real
part, 7 imaginary part
5. 6 2 11i real part, 6; imaginary part, 211i
6. 224i 2 8 7. 22 1 26i 8. 85
9. 3
} 2
2 i
} 10.
2 1
} 1
5 3i
} 11. 1 1 3i
5
12–15.
imag.
5i
Algebra 2
Chapter 4 Resource Book
i
22i
1
1 1 3i
real
2 2 i
12. 2 13. 5 14. Ï }
10 15. Ï }
5
Challenge Practice
1. Sample answer: x 2 1 25 5 0 2. Sample
answer: (x 1 3) 2 1 8 5 0 3. 1 4. 21
5. False. If the complex number is real, the
number equals its conjugate. 6. False. Sample
answer: The sum of two imaginary numbers can
be a real number or an imaginary number. For
example, the sum of 4 1 2i and 3 2 2i is 7, which
is a real number.
7. True. (a 1 bi)(a 2 bi) 5 a2 2 bi 1 bi 2 bi2 5 a2 2 b2 (21) 5 a2 1 b2 , which is a real
number. 8. True. The absolute value of a 1 bi is
Ï }
a2 1 b2 and the absolute value of its conjugate
a 2 bi is Ï }
a2 1 (2b) 2 5 Ï }
a2 1 b2 .
9. Sum of complex numbers: a 1 bi 1 c 1 di 5
(a 1 c) 1 (b 1 d)i; Complex conjugate of sum:
(a 1 c) 2 (b 1 d)i; Sum of complex conjugates:
a 2 bi 1 c 2 di 5 (a 1 c) 2 (b 1 d)i
10. Product of complex numbers: (a 1 bi) p
(c 1 di) 5 ac 1 adi 1 bci 1 bdi2 5 (ac 2 bd) 1
(ad 1 bc)i; Complex conjugate of product:
(ac 2 bd) 2 (ad 1 bc)i; Product of complex
conjugates: (a 2 bi)(c 2 di) 5 ac 2 adi 2 bci 1
bdi2 5 (ac 2 bd) 2 (ad 1 bc)i 11. h ≤ h0 Lesson 4.7
Practice Level A
1. 24, 2 2. 24, 22 3. 22, 6 4. 3, 7
5. 7 6 Ï }
7 6. 210 6 2 Ï }
3 7. 2 1
} ,
2 3
}
2
8. 24 6 Ï }
7 9. 2 7
} ,
2 1
} 10. 4; (x 1 2)
2 2
11. 1; (x 2 1) 2 12. 81; (x 1 9) 2
13. 144; (x 1 12) 2 14. 49; (x 2 7) 2
15. 25
}
4 ; 1 x 2 5
}
2 2 2
16. 1
} ;
4 1 x 1 1
}
2 2 2
17. 49
}
4 ; 1 x 1 7
}
2 2 2
18. 1 6 Ï }
3 19. 23 6 Ï }
6
20. 24 6 3 Ï }
2 21. 21 6 2i 22. 25 6 Ï }
14
23. 7 6 Ï }
39 24. 1
} 6
2 Ï} 3 1
} i 25. } 6
2 2 Ï} 13
}
2
26. y 5 (x 1 4) 2 2 11; (24, 211)
27. y 5 (x 2 6) 2 2 35; (6, 235)
28. y 5 (x 1 2) 2 1 8; (22, 8)
29. y 5 (x 2 5) 2 2 22; (5, 222) 30. 5 31. 6
32. 4 33. 10
Practice Level B
1. 27, 21 2. 22, 8 3. 21, 13 4. 21, 7
5. 2 5
} ,
2 7
} 6. 2 6 Ï
2 }
7 7. 2 2
} ,
3 4
} 8. 2
3 3
} 6 Ï
4 }
3
9. 2 2
} 6
3 Ï} 5
} 10. 16; (x 1 4)2
3
11. 121; (x 2 11) 2 12. 64; (x 1 8) 2
13. 9
} ;
4 1 x 1 3
}
2 2 2
14. 81
}
4 ; 1 x 2 9
}
2 2 2
15. 4; (3x 2 2) 2 16. 22 6 Ï }
5 17. 5 6 Ï }
15
18. 1 6 Ï }
10 19. 23 6 i 20. 24 6 2 Ï }
3
21. 26 6 Ï }
22 22. 12 6 3 Ï }
7 23. 2 5
}
2
24. 1
} 6
2 Ï} 11
} i 25. 21, 3
2
26. y 5 (x 1 7) 2 2 38; (27, 238)
27. y 5 (x 2 4) 2 2 6; (4, 26)
28. y 5 2(x 1 1) 2 2 7; (21, 27)
29. y 5 3 1 x 2 3
}
2 2 2 1 45
}
4 ; 1 3
} ,
2 45
}
4 2
30. 7 31. 8 32. 55.4 ft
Practice Level C
1. 2 2
} , 2 2. 2
3 3
} ,
2 13 3
} 3. 2 } ,
2 5 11 3 Ï} 7
} 4. 2 } 6 }
15 10 5
5. 20.7 6 Ï }
3 6. 23, 8 7. 24 6 Ï }
17
8. 8 6 2 Ï }
11 9. 3
} 6
2 Ï} 37 7
} 10. 2 } 6
2 2 Ï} 11
}
2 i
11. 22 12. 2 3
} 6
2 Ï} 7
} i 13. 4 6 Ï} 7
2
14. 26, 1 15. 2 5
} 6
2 3
} i 16.
2 7
} 6
6 Ï} 109
}
6
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