Question 1

Perform the operation shown below and leave the result in trigonometric form.

Accepted Answer

A)   
B)   
C)   
D)   
E)    C

Question 2

Use DeMoivre's Theorem to find the indicated power of the following complex number.

Accepted Answer

A)  -324
B)  729
C)  324
D)  2,916
E)  243 A

Question 3

Find the product  using trigonometric forms. Leave the result in trigonometric form.

Accepted Answer

A)   
B)   
C)   
D)   
E)    E

Question 4

Find the standard form of the complex number  . Round values to the nearest hundredth.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 5

Represent the complex number below graphically.

Accepted Answer

A)    
B)   
C)   
D)   
E)

Question 6

Plot the following complex number. 
-

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 7

Find the cube roots of the following complex number. Write each of the roots in standard form.

Accepted Answer

A)    ,  , 
B)    , 
C)   
D)    ,  , 
E)    ,  ,

Question 8

Find the trigonometric form of the complex number shown below.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 9

The vector  gives the number of units of two models of laptops produced by a company. The vector  gives the prices (in dollars) of the two models of laptops, respectively. Identify the vector operation used to increase revenue by 5%.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 10

Given vectors  and  determine the quantity indicated below.

Accepted Answer

A)  -12
B)  -180
C)  10
D)  60
E)  -70

Question 11

Find the trigonometric form of the complex number shown below.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 12

Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 13

Use the dot product to find the magnitude of u if

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 14

Find the standard form of the complex number shown below. Round answers to two decimal places.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 15

Find the fourth roots of  Write the roots in trigonometric form.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 16

Divide the complex numbers below and leave the result in trigonometric form.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 17

Find all solutions to the following equation.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 18

Perform the operation shown below and leave the result in trigonometric form.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 19

Find the angle between the vectors u and v.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 20

Given that Force 1 = 70 pounds and Force 2 = 120 pounds, find the angle between the forces if the magnitude of the resultant force is 90 pounds. Round answer to the nearest degree.

Accepted Answer

A)  60°
B)  40°
C)  53°
D)  45°
E)  48°

Exam 5: Linear Systems and Matrices

Perform the operation shown below and leave the result in trigonometric form.

Use DeMoivre's Theorem to find the indicated power of the following complex number.

Find the product using trigonometric forms. Leave the result in trigonometric form.

Find the standard form of the complex number . Round values to the nearest hundredth.

Represent the complex number below graphically.

Plot the following complex number. -3

Find the cube roots of the following complex number. Write each of the roots in standard form.

Find the trigonometric form of the complex number shown below.

The vector gives the number of units of two models of laptops produced by a company. The vector gives the prices (in dollars) of the two models of laptops, respectively. Identify the vector operation used to increase revenue by 5%.

Given vectors and determine the quantity indicated below.

Find the trigonometric form of the complex number shown below.

Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form.

Use the dot product to find the magnitude of u if

Find the standard form of the complex number shown below. Round answers to two decimal places.

Find the fourth roots of Write the roots in trigonometric form.

Divide the complex numbers below and leave the result in trigonometric form.

Find all solutions to the following equation.

Perform the operation shown below and leave the result in trigonometric form.

Find the angle between the vectors u and v.

Given that Force 1 = 70 pounds and Force 2 = 120 pounds, find the angle between the forces if the magnitude of the resultant force is 90 pounds. Round answer to the nearest degree.