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GP1-‐CA-‐S1-‐HW7
Last name:
_______________________________ Period: _____
Seat #: _______
Test on Thursday August 20 Skill
1 Review
Selected Solutions Simplify the
following radicals using the
imaginary unit 1.
−72
1. 6𝑖 2
Solution −72
= 𝑖 36 ∙ 2
= 6𝑖 2
Evaluate:
4. 𝑖!"
4. −𝑖
Solution 15÷ 4 = 3.75 The remainder is
3, therefore 𝑖!" = −𝑖 5.
𝑖!!
5. −1
Solution 15÷ 4 = 16.5 The remainder is
2, therefore 𝑖!! = −1 9.
12− 5𝑖 − 16+ 7𝑖 + (1+ 2𝑖)
9. −3− 10𝑖
Solution = 12− 5𝑖 − 16− 7𝑖 + 1+ 2𝑖
= 12− 16+ 1− 5𝑖 − 7𝑖 + 2𝑖
= −3− 10𝑖 11. −3𝑖(7− 8𝑖)
11.
−24− 21𝑖
Solution = −21𝑖 + 24𝑖!
= −21𝑖 + 24 −1
= −24− 21𝑖
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GP1-‐CA-‐S1-‐HW7
Last name:
_______________________________ Period: _____
Seat #: _______
13. (6+ 2𝑖)(−1+ 𝑖)(3− 2𝑖)
13. −16+ 28𝑖
Solution −1 𝑖 6 −6 6𝑖
2𝑖 −2𝑖 2𝑖! 6+ 2𝑖 −1+ 𝑖 = −8+ 4𝑖
So, −8+ 4𝑖 3− 2𝑖 3
−2𝑖 −8 −24 16𝑖 4𝑖 12𝑖 −8𝑖!
−8+ 4𝑖 3− 2𝑖 = −16+ 28𝑖 14.
6 3− 5𝑖 − 8𝑖(2− 𝑖)
14. 10− 46𝑖
Solution = 18− 30𝑖 − 16𝑖 + 8𝑖! = 18− 8−
30𝑖 − 16𝑖 = 10− 46𝑖
18. Multiply the complex
number −5− 8𝑖 by the complex
conjugate. 18. 89
Solution −5− 8𝑖 −5+ 8𝑖 = −5 ! + 8! = 89
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GP1-‐CA-‐S1-‐HW7
Last name:
_______________________________ Period: _____
Seat #: _______
Evaluate:
19. (1− 3𝑖)!
19. −26+ 18𝑖
Solution 1− 3𝑖 1− 3𝑖 1
−3𝑖 1 1 −3𝑖 −3𝑖 −3𝑖 9𝑖!
1− 3𝑖 1− 3𝑖 = −8− 6𝑖 So, 1− 3𝑖 ! =
1− 3𝑖 1− 3𝑖 1− 3𝑖 = −8− 6𝑖 1− 3𝑖
1 −3𝑖 −8 −8 24𝑖 −6𝑖
−6𝑖 18𝑖! = −26+ 18𝑖
20. (7+ 2𝑖)(2− 5𝑖)(2+ 5𝑖)(7− 2𝑖)
20. 1537
Solution = 7+ 2𝑖 7− 2𝑖 2− 5𝑖 2+ 5𝑖 = 7! + 2!
2! + 5! = 53 29 = 1537
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GP1-‐CA-‐S1-‐HW7
Last name:
_______________________________ Period: _____
Seat #: _______
23. !!!
!"!!!
23. !
!
Solution
=7− 1𝑖14− 2𝑖
14+ 2𝑖14+ 2𝑖
14 2𝑖 7 98 14𝑖
−1𝑖 −14𝑖 −2𝑖!
=100
14! + 2!
=12
25. !!!!!
25. !"!"+ !"
!"𝑖
Solution
=7
3− 2𝑖3+ 2𝑖3+ 2𝑖
=21+ 14𝑖3! + 2!
=2113+
1413 𝑖
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GP1-‐CA-‐S1-‐HW7
Last name:
_______________________________ Period: _____
Seat #: _______
Evaluate:
26. !!!!!!!
+ !!!!!!!
26.
!"!"+ !!"
!"𝑖
Solution
=6− 4𝑖3+ 1𝑖
3− 1𝑖3− 1𝑖 +
8− 1𝑖1+ 3𝑖
1− 3𝑖1− 3𝑖
3 −1𝑖 1 −3𝑖
6 18 −6𝑖 8 8 −24𝑖
−4𝑖 −12𝑖 4𝑖! −1𝑖 −1𝑖
3𝑖!
=14− 18𝑖3! + 1! +
5− 25𝑖1! + 3!
=19− 43𝑖
10
=1910+
−4310 𝑖
27. !!!!!!!
− !!!!!!!!
27.
!"!"+ !"
!"𝑖
Solution
=8− 1𝑖 − 6− 7𝑖
4+ 3𝑖
=2+ 6𝑖4+ 3𝑖
4− 3𝑖4− 3𝑖
4 −3𝑖 2 8 −6𝑖 6𝑖
24𝑖 −18𝑖!
=26+ 18𝑖4! + 3!
=26+ 18𝑖
25
=2625+
1825 𝑖
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GP1-‐CA-‐S1-‐HW7
Last name:
_______________________________ Period: _____
Seat #: _______
29. !"!!"!
!!!!
29. 26
Solution 16+ 28𝑖6− 2𝑖
6+ 2𝑖6+ 2𝑖
6 2𝑖 16 96 32𝑖
28𝑖 168𝑖 56𝑖!
=40+ 200𝑖6! + 2!
=4040+
20040 𝑖
= 1+ 5𝑖 So, !"!!"!
!!!!= 1+ 5𝑖 = 1! + 5! = 26
30. −15+ 8𝑖
30. 17
Solution = −15 ! + 8! = 289
= 17 31.
(9− 2𝑖)(4+ 9𝑖)
31. 8245
Solution 4 9𝑖 9 36 81𝑖
−2𝑖 −8𝑖 −18𝑖! = 54+ 73𝑖
= 54! + 73! = 8245 Note:
8245 = 5 ∙ 17 ∙ 97
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GP1-‐CA-‐S1-‐HW7
Last name:
_______________________________ Period: _____
Seat #: _______
Plot each complex number in the
complex plane:
32. −1 + 𝑖
Plot −1, 1
34. − 4𝑖
Plot 0,−4