Question 1

Write the complex number in standard form. ​   ​
​

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

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

Accepted Answer

A)    ​ 
B)    
C)    ​ 
D)    ​ 
E)    
A)    ​ 
B)    
C)    ​ 
D)    ​ 
E)

Question 4

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

Accepted Answer

A)    ​ 
B)    ​ 
C)    ​ 
D)    ​ 
E)    
A)    ​ 
B)    ​ 
C)    ​ 
D)    ​ 
E)

Question 5

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

Accepted Answer

A) ​   ​   
B) ​   ​   
C) ​   ​   
D) ​   ​   
E) ​   ​   
A) ​   ​   
B) ​   ​   
C) ​   ​   
D) ​   ​   
E) ​   ​

Question 6

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

Question 7

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)    
A)    
B)    
C)    
D)    
E)

Question 8

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

Accepted Answer

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

Question 9

​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))) 
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)))

Question 10

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)    
A)    ​ 
B)    ​
​ 
C)    ​ 
D)    ​ 
E)

Question 11

Represent the complex number below graphically.

Accepted Answer

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

Question 12

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 above 
A) 0.8767-1.7976i 
B) -1.7976​ - 0.8767i 
C) ​-1.7976 + 0.8767i 
D) ​-0.8767-1.7976i 
E) None of the above

Question 13

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

Accepted Answer

A) ​   
B) ​   
C)    
D)    
E)    
A) ​   
B) ​   
C)    
D)    
E)

Question 14

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   
A) 4   
B) 2   
C) 8   
D) 4   
E) 8

Question 15

Simplify the expression. ​
I -14
​

Accepted Answer

A) i 
B) -3i 
C) -i 
D) -1 
E) 1 
A) i 
B) -3i 
C) -i 
D) -1 
E) 1

Question 16

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

Accepted Answer

A) -3 
B)    
C)    
D)    
E)    
A) -3 
B)    
C)    
D)    
E)

Question 17

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

Accepted Answer

A) ​256 
B) -64 
C) 64 
D) 16 
E) -256 
A) ​256 
B) -64 
C) 64 
D) 16 
E) -256

Question 18

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

Accepted Answer

A) 31 
B) 27 
C) 28 
D) 29 
E) 30 
A) 31 
B) 27 
C) 28 
D) 29 
E) 30

Question 19

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) 1 
A) - 20 
B) 20 
C) -1 
D)    
E) 1

Question 20

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

Accepted Answer

A)    ​ 
B)    ​ 
C)    ​ 
D)    ​ 
E)    
A)    ​ 
B)    ​ 
C)    ​ 
D)    ​ 
E)

Write the complex number in standard form.

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

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

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

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

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

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

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

Find the trigonometric form of the complex number shown below.

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

Represent the complex number below graphically.

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

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

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

Simplify the expression. I ^-14

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

Raise the complex number to the fourth power. 4i

Perform the operation and write the result in standard form.

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

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

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Exam 4: Complex-Numbers

Write the complex number in standard form. ​ ​ ​

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

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

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

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

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

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

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

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

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

Represent the complex number below graphically.

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

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

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

Simplify the expression. ​ I -14 ​

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

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

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

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

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

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Write the complex number in standard form.

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

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

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

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

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

Find the trigonometric form of the complex number shown below.

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

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

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

Simplify the expression. I ^-14

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

Raise the complex number to the fourth power. 4i

Perform the operation and write the result in standard form.

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

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