Deck 5: Linear Systems and Matrices

Question 1

Find the trigonometric form of the complex number represented graphically.

A)
B)
C)
D)
E)

Answer 1

Question 2

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.

A)60°
B)40°
C)53°
D)45°
E)48°

Answer 2

48°

Question 3

Find the absolute value of the complex number .

A)
B)
C)
D)
E)

Answer 3

Question 4

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

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

Question 5

Write the complex number shown below in trigonometric form.

A)

B)

C)

D)

E)

Question 6

Find the trigonometric form of the complex number shown below.

A)

B)

C)

D)

E)

Question 7

Find the angle between the vectors u and v.

A)
B)
C)
D)
E)

Question 8

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

A)


B)


C)


D)


E)

Question 9

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

A)
B)
C)
D)
E)

Question 10

Given vectors and determine the quantity indicated below.

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

Question 11

Plot the following complex number.
-3

A)
B)
C)
D)
E)

Question 12

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

A)


B)


C)


D)


E)

Question 13

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

A)
B)
C)
D)
E)

Question 14

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%.

A)
B)
C)
D)
E)

Question 15

Represent the complex number below graphically.

A)


B)


C)


D)


E)

Question 16

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

A)
B)
C)
D)
E)

Question 17

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

A)
B)
C)
D)
E)

Question 18

Use the dot product to find the magnitude of u if

A)
B)
C)
D)
E)

Question 19

Find the trigonometric form of the complex number shown below.

A)
B)
C)

D)

E)

Question 20

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

A)
B)
C)
D)
E)

Question 21

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

A)


B)

C)


D)


E)

Question 22

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

A)32
B)64
C)
D)
E)-64

Question 23

Find all solutions to the following equation.

A)


B)


C)


D)


E)

Question 24

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

A)
, ,

B) ,

C)

D)
, ,

E)
, ,