Question 1

Use DeMoivre's theorem to find the indicated roots of the complex number. ​
Cube roots of  ​

Accepted Answer

A)    ​
B)    ​
C)    ​
D)    ​
E)   F) C) and D)
G) A) and D)

Question 2

Find the fifth roots of the following complex number.Express the root(s)  in trigonometric form. ​

Accepted Answer

A)  -3
B)   
C)   
D)   
E)   F) A) and D)
G) C) and E)

Question 3

Perform the addition or subtraction and write the result in standard form. ​  ​

Accepted Answer

A)  ​ 
B)  ​ 
C)   
D)   
E)   F) A) and B)
G) A) and C)

Question 4

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)   F) A) and B)
G) B) and D)

Question 5

Use DeMoivre's theorem to find the indicated roots of the complex number. ​
Cube roots of  ​

Accepted Answer

A)    ​
B)   
C)    ​
D)    ​
E)   F) B) and D)
G) A) and C)

Question 6

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

Accepted Answer

A)   
B)   
C)   
D)   
E)   F) B) and E)
G) B) and C)

Question 7

Use DeMoivre's theorem to find the indicated roots of the complex number. ​
Fourth roots of  ​

Accepted Answer

A)    ​
B)    ​
C)    ​
D)    ​
E)   F) B) and E)
G) All of the above

Question 8

Plot the complex number and find its absolute value. ​
-5 + 2i
​

Accepted Answer

A)  ​  ​ 
B)  ​  ​ 
C)  ​  ​ 
D)  ​  ​ 
E)  ​  ​ F) B) and E)
G) C) and D)

Question 9

Perform the operation and write the result in standard form. ​  ​

Accepted Answer

A)  31
B)  27
C)  28
D)  29
E)  30F) A) and B)
G) C) and D)

Question 10

Simplify the expression. ​
I -14
​

Accepted Answer

A)  i
B)  -3i
C)  -i
D)  -1
E)  1F) A) and E)
G) None of the above

Question 11

Write the complex number in standard form. ​  ​
​

Accepted Answer

A)   
B)   
C)    
D)   
E)   F) None of the above
G) B) and D)

Question 12

​Find the trigonometric form of the complex number shown below. ​  ​

Accepted Answer

A)  ​  (cos (arctan (-  ) )  + i sin (arctan (-  ) ) ) 
B)  ​​  (cos (arctan (  ) )  + i sin (arctan (  ) ) ) 
C)  ​​  (cos (arctan (-  ) )  + i sin (arctan (-  ) ) ) 
D)  ​​  (cos (arctan (-  ) )  + i sin (arctan (-  ) ) ) 
E)  ​​  (cos (arctan (4) )  + i sin (arctan (4) ) ) F) C) and E)
G) A) and C)

Question 13

Represent the complex number below graphically.

Accepted Answer

A)   
B)   
C)   
D)   
E)   F) D) and E)
G) A) and B)

Question 14

Use a graphing utility to represent the complex number in standard form.Round your answer to 4 decimal places. ​  ​

Accepted Answer

A)  0.8767-1.7976i
B)  -1.7976​ - 0.8767i
C)  ​-1.7976 + 0.8767i
D)  ​-0.8767-1.7976i
E)  None of the aboveF) A) and C)
G) B) and D)

Question 15

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

Accepted Answer

A)  - 20
B)  20
C)  -1
D)   
E)  1F) C) and E)
G) A) and E)

Question 16

Raise the complex number to the fourth power. ​
​4i
​

Accepted Answer

A)  ​256
B)  -64
C)  64
D)  16
E)  -256F) B) and C)
G) A) and C)

Question 17

Find the trigonometric form of the complex number shown below. -4 + 4  i

Accepted Answer

A)  4 
B)  2 
C)  8 
D)  4 
E)  8 F) C) and E)
G) B) and D)

Question 18

Use DeMoivre's theorem to find all the solutions of the equation and represent the solutions graphically.(Round your answer to four decimal places.)  ​  ​

Accepted Answer

A)    ​
B)    ​​
C)    ​
D)    ​
E)   F) A) and B)
G) A) and C)

Question 19

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

Accepted Answer

A)   
B)   
C)   
D)   
E)   F) None of the above
G) A) and E)

Question 20

Do the operation and express the answer in a + bi form. ​  ​

Accepted Answer

A)  - 8 + 14i
B)  8 + 7i
C)  - 8 + 7i
D)  - 8 - 7i
E)  8 - 7iF) C) and D)
G) B) and D)

Exam 4: Complex-Numbers

Use a graphing utility to represent the complex number in standard form.Round your answer to 4 decimal places. ​ ​

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Find the fifth roots of the following complex number.Express the root(s) in trigonometric form. ​

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Use DeMoivre's theorem to find the indicated roots of the complex number. ​ Fourth roots of ​

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Use DeMoivre's theorem to find the indicated roots of the complex number. ​ Cube roots of ​

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Plot the complex number and find its absolute value. ​ -5 + 2i ​

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Simplify the expression. ​ I -14 ​

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Use DeMoivre's theorem to find the indicated roots of the complex number. ​ Cube roots of ​

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

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Perform the operation and write the result in standard form. ​ ​

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

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Raise the complex number to the fourth power. ​ ​4i ​

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Represent the complex number below graphically.

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Write the complex number in standard form. ​ ​ ​

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Perform the addition or subtraction and write the result in standard form. ​ ​

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​Find the trigonometric form of the complex number shown below. ​ ​

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

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

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Use DeMoivre's theorem to find all the solutions of the equation and represent the solutions graphically.(Round your answer to four decimal places.) ​ ​

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Do the operation and express the answer in a + bi form. ​ ​

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Find the trigonometric form of the complex number shown below. -4 + 4 i

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Use a graphing utility to represent the complex number in standard form.Round your answer to 4 decimal places.

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Find the fifth roots of the following complex number.Express the root(s) in trigonometric form.

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Use DeMoivre's theorem to find the indicated roots of the complex number. Fourth roots of

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Use DeMoivre's theorem to find the indicated roots of the complex number. Cube roots of

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Plot the complex number and find its absolute value. -5 + 2i

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Simplify the expression. I ^-14

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Use DeMoivre's theorem to find the indicated roots of the complex number. Cube roots of

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

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Perform the operation and write the result in standard form.

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Raise the complex number to the fourth power. 4i

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Write the complex number in standard form.

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Perform the addition or subtraction and write the result in standard form.

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Find the trigonometric form of the complex number shown below.

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

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Use DeMoivre's theorem to find all the solutions of the equation and represent the solutions graphically.(Round your answer to four decimal places.)

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Do the operation and express the answer in a + bi form.

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