ISM: Precalculus Chapter]

4. (-7 + 51)- (-9 - 11i) = -7 + 5i + 9 + 11i=-7+9+5i+11i= 2 + 16i

19. (2+3i)2 =4+12i+9i2

= 4+ 12i-9=-5+12i

5. 6-(-5 +4i) -(-13 - i) = 6 + 5 -4i + 13+ i= 24-3i 20. (5-2i)2 =25-20i+4i2

= 25-20i-4= 21-20i

6. 7 - (-9 + 2i) - (-17 - i) = 7 + 9 --2i + 17+ i=33-i

7. 8i - (14 - 9i) = 8i - 14 + 9i=-14+8i+9i=-14+17i

2 2 3+i-=----3-i 3-i 3+i

2(3 + i)

9+1=2(3+i)

103+i

53 1_

=-+-15 5

21.

8. 15i - (12 - 11i) = 15i - 12 + 11i=-12+15i+11i=-12+26i

9. -3i(7i - 5) = -21i2 + 15i= -21(-1) + 15i= 21 + 15i

10. -8i(2i-7)=-16i2+56i =-16(-1)+56i=9-25i2 =9+25=34= 16+56i 22.

3 3 4-i--=-----4+i 4+i 4-i

3(4-i)16-i2

=3(4-i)17

12 3_=---1

17 17

11. (-5 +4i)(3+ i) = -15 -5i + 12i +4;2=-15+7i-4=-19+7i

12. (-4 - 8i)(3 + i) = -12 - 4i - 24i - 8i2

=-12-28i+8= -4-28i

13. (7-5i)(-2-3i) =-14-2li+10i+15i2

=-14 -15 -l1i=-29-1li

2i 2i 1- i23. -=---

l+i l+i l-i2i - 2i2 = 2 + 2i = 1+ i

1+1 2

14. (8-4i)(-3 +9i)=-24+72i+12i-36i2

= -24 + 36 + 84i= 12 + 84i

24.5i 5i 2 + i

--=-----2-i 2-i 2+ i

10i+ 5i2

4+1-5 + 10i

5= -1+2i

15. (3 + 5i)(3 - 51)

16. (2+7i)(2-7i)=4-49i2 =4+49=53

17. (-5 + i)(-5-i) = 25+5i-5i _i2

=25+1=26

18. (-7 + i)(-7 - i) = 49 + 7i - 7i - i2

=49+1=50

265

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Chapter 2 ISM: Precalculus

33. (-2 +.J-4f = (-2 +2i)2

= 4-8i +4i2=4 - 8i-4=-8i

25.8i 8i 4 +3i

--=--.--4-3i 4-3i 4+3i

32i + 24i216+9

-24+32i25

24 32.=--+-/

25 25

34. (-5-.J=9f =(-5-i~)2 = (-5-3i)2

= 25+ 30i +9i2

= 25 + 30i - 9= 16+ 30i

35. (-3-Hf = (-3-i.J7f

=9+6i.J7 +i2(7)= 9-7 +6i.J7

= 2+6i.J7

-6i -6i 3-2i -18i+12i226. __ = __ .__3+2i 3+2i 3- 2i 9+4

-12-18i 12 18.---=----/

13 13 13

27.2+3i 2+3i 2 - i--=--.-2+i 2+i 2-i

4 +4i -3i24+1

7 +4i5

7 4.=-+-/

5 5

36. (-2 + f-lif = (-2 + i-Jilf

= 4 - 4i-Jil + i2(11)

= 4 -11- 4i-Jil

= -7 -4i-Jil

-12+Hs -12+i.J2832 32

-12+2i.J7 3.J7 .----=--+-/

32 8 16

28. 3- 4i 3- 4i 4 - 3i--=--.--4+3i 4+3i 4-3i

12- 25i+12i216+9

-25i25

= -i

-8+.J-3237.

24

29. .J-64 -.J-25 = i.J64 -i.J2s

= 8i-5i = 3i 38.

30 . .J-81-.J-144 =iJ81-iM4 =9i-12i=-3i

31. 5.J-16 +3.J-81 = 5(4i) + 3(9i)=20i+27i=47i 39. -6-r-I2

48

32. 5H +3.J-18

= 5i-J8+3i.J18 = 5i#2 +3im

= 1Oi.fi +s.Ji= 19i.fi

266

-8+i.J32

24-8 + i.J16:2

24-8 + 4i.fi

241 .fi.

=--+-/3 6

-12+i#732

-6-i.J!2

48-6-iM

48-6-2i.J3

481 .J3.

=----/8 24

© 2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist.No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

ISM: Precalculus Chapter 2

-15--1-18 -15-i.J!840.33 33

-15-3iF2 5 F2.=----/

33 11 11

-15-iJ9:"233

46. x2 - 2x + 17 = 0

2±~(-2)2 -4(1)(17)x=

2(1)

2±~x=2

2±.J-64x=

22±8ix=--

2x = 1±4i

The solution set is {I+ 4i,1- 4i}.

41. F-8(.J=3--I5)=i../8(i.[3--I5)

=2iF2(i.[3 - -15)=-2.J6 - 2iJiO

42. -1-12 (r-4 -F2) = iM(iJ4 -F2)=2i.[3(2i- F2)= 4i2.[3- 2i.J6= -4.[3 - 2i.J6

45. x2- 6x+ 10 = 0

6±~(-6)2 -4(1)(10)x=

2(1)

6±~x=2

6±,J-4x=

26±2ix=--

2x=3±i

The solution set is {3+ i, 3 - i}.

47. 4x2+8x+13 = 0r----

-8±~82 -4(4)(13)x=

2(4)

-8 ± -164- 2088

-8±../-l44

8-8± 12i

84(-2±3i)

8-2±3i

=--2

=-l±~i2

The solution set is {-I+%i,-1-%i}.

43. (3H)( -4-1-12 ) = (3i-l5)(-8i.[3)

=-24i2J15=24J15

44.(3~)(2~)=(3i.J7)(2i../8)= (3i.J7)(2i#2)

= (3i.J7)(4iF2) = 12;2M= -12M

267

©2007Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist.No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

~- ~i}o2 2

3 3o 0 {2 .J14 0 2 .Jl4 o}The solution set IS -+_1, ---I 0

3 3 3 3

51. (2-3i)(I-i)-(3-i)(3+i)

= (2 - 2i - 3i + 3i2) - (32 _ i2 )

= 2-Si+3i2 -9+i2

= -7 -Si +4i2

= -7-5i+4( -I)= -II-Si

52. (8 + 9i)(2 - i) - (1- i)(1 + i)

=(16-8i+18i-9i2)_(12 _i2)

= 16 + IOi- 9i2- 1+ i2

= IS +!Oi -8i2

= IS + !Oi - 8(- I)

= 23 + IOi

53. (2+i)2 -(3 -iY= (4 + 4i + i2

) - (9 - 6i + i2 )

= 4 + 4i + i2 - 9 + 6i _ j2

= -S+!Oi