Problem 1

240 Exp@I Π � 6.D - 240 Exp@-I Π � 2D207.846+ 360. ä

Abs@%D415.692

Arg@%%D 180 � Π

60.

or

240 Sqrt@3.Dor

415.692

angle = 30 + 30

60

Problem 2

H240 Exp@I Π 5 � 6.D - 240 Exp@-I Π � 2DL207.846- 360. ä

Abs@%D415.692

Arg@%%D 180 � Π

-60.

or

240 Sqrt@3.Dor

415.692

angle = 30 + 30 - 120

-60

Problem 3

H240 Exp@I Π 5 � 6.D - 240 Exp@I Π � 6DL

-415.692 + 9.9476 ´ 10-14

ä

Abs@%D415.692

Arg@%%D 180 � Π

180.

Problem 4

Vab

200 ´ 72 � 70 HExp@I Π � 6.D - Exp@-I Π � 2DL178.154+ 308.571 ä

Abs@%D356.308

Arg@%%D 180 � Π

60.

Problem 5

Vbc

200 ´ 72 � 70 HExp@-I Π � 2D - Exp@I 5 Π � 6.DL178.154- 308.571 ä

Abs@%D356.308

Arg@%%D 180 � Π

-60.

Problem 6

Vca

200 ´ 72 � 70 HExp@I 5 Π � 6.D - Exp@I Π � 6.DL

-356.308 + 7.99361 ´ 10-14

ä

Abs@%D356.308

Arg@%%D 180 � Π

180.

Problem 7

Solve@16 H1 + IL � H21 + 17.7 IL Van � 240 Exp@I Π � 3D, VanD88Van ® 166.559+ 238.989 ä<<

Abs@166.55912874366487`+ 238.98887344843325` äD291.303

2 Ch11HW.nb

Arg@166.55912874366487`+ 238.98887344843325` äD 180 � Π

55.1261

Problem 8

% - 120

-64.8739

Vbn = 291.3 Angle - 64.9

Problem 9

55.1 + 120

175.1

Vcn = 291.3 Angle 175.1`

Clear@Vp, ΘaD

Problem 10

Solve@8Vp Cos@ΘaD - Vp Cos@Θa - 2 � 3 ΠD � 200 Cos@Π � 6D,

Vp Sin@ΘaD - Vp Sin@Θa - 2 � 3 ΠD � 200 Sin@Π � 6D<, 8Vp, Θa<D �� N

Solve::ifun:

Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information.

�

88Vp ® -115.47, Θa ® -3.14159<, 8Vp ® -115.47, Θa ® 3.14159<, 8Vp ® 115.47, Θa ® 0.<<

Vp = 115.47005383792516`; Θa = 0;

Vp Exp@I ΘaD115.47

or

200 � Sqrt@3.Dor

115.47

Solve@115.47 H24 + I 3L � H24. + I 3 + xL � 100, xD88x ® 3.7128+ 0.4641 ä<<

Vp Exp@I ΘaD H24 + 3 IL2771.28+ 346.41 ä

Expand@100 H24 + 3 I + R + I XLDH2400 + 300 äL + 100 R + 100 ä X

Solve@82771.281292110204` == 2400 + 100 R, 346.4101615137755` == 300 + 100 X<, 8R, X<D88R ® 3.71281, X ® 0.464102<<

Ch11HW.nb 3

Clear@Vp, ΘaD

Van = 208 � Sqrt@3D Exp@I H� 3 - � 6LD �� N

104.+ 60.0444 ä

Abs@VanD120.089

Vbn = Van Exp@-I 2 � 3 ΠD �� N

1.9703 ´ 10-14

- 120.089 ä

VAN = Van H7 + 5 IL � H7.6 + 5.4 IL95.8213+ 55.6415 ä

VAN Sqrt@3D Exp@ I Π � 6D95.545+ 166.446 ä

Abs@%D191.92

Arg@%%D 180 � Π

60.1429

VAN :

H7 + 5 IL � H7.6 + 5.4 IL 208 � Sqrt@3.D Exp@I Π � 6D95.8213+ 55.6415 ä

Abs@%D110.805

Arg@%%D 180 � Π

30.1429

VAB = 110.805 Sqrt@3.D Exp@I 60.1439 Π � 180D95.5422+ 166.448 ä

4 Ch11HW.nb