Question 1

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 2

Find the trigonometric form of the complex number shown below.

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 power of the complex number.Write the result in standard form.

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

Solve the equation and write complex solutions in standard form. ​   ​

Accepted Answer

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

Question 7

​Find the absolute value of the complex number 5 + 3i. ​

Accepted Answer

A) ​   
B) ​34 
C) ​   
D) ​5 + 3​i 
E) ​   
A) ​   
B) ​34 
C) ​   
D) ​5 + 3​i 
E) ​

Question 8

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

Accepted Answer

A) 19i 
B) - 19i 
C) - 190i 
D) - 19 
E) 19 
A) 19i 
B) - 19i 
C) - 190i 
D) - 19 
E) 19

Question 9

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

Accepted Answer

A) ​-1.29 - 1.53i 
B) ​-2.53 - 2.88i 
C) ​-2.04 - 2.63i 
D) ​-1.52 - 1.92i 
E) ​-2.71 - 3.06i 
A) ​-1.29 - 1.53i 
B) ​-2.53 - 2.88i 
C) ​-2.04 - 2.63i 
D) ​-1.52 - 1.92i 
E) ​-2.71 - 3.06i

Question 10

Represent the complex number graphically, and find the trigonometric form of the number. ​
-8i
​

Accepted Answer

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

Question 11

Perform the indicated operation in trigonometric form.Write the solution in standard form rounded to four decimal places.   ​

Accepted Answer

A) 0.4682 + 0.2027i 
B) 0.4777 - 0.1791i 
C) 0.7197 + 0.6943i 
D) 0.5095 + 0.0254i 
E) 0.3672 + 0.3542i 
A) 0.4682 + 0.2027i 
B) 0.4777 - 0.1791i 
C) 0.7197 + 0.6943i 
D) 0.5095 + 0.0254i 
E) 0.3672 + 0.3542i

Question 12

Find all the zeros of the function and write the polynomial as a product of linear factors. ​   ​

Accepted Answer

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

Question 13

Solve the equation and write complex solutions in standard form. ​
​   ​

Accepted Answer

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

Question 14

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

Accepted Answer

A) 23 
B) 1 
C) -1 
D)    
E) -23 
A) 23 
B) 1 
C) -1 
D)    
E) -23

Question 15

Find a polynomial function with real coefficients that has the given zeros. ​   ​

Accepted Answer

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

Question 16

Determine the number of solutions of the equation in the complex number system. ​   ​

Accepted Answer

A)    has degree 0 so there are no solutions in the complex number system. 
B)    has degree 4 so there are four solutions in the complex number system. 
C)    has degree 2 so there are two solutions in the complex number system. 
D)    has degree   so there are four solutions in the complex number system. 
E)    has degree -4 so there are no solutions in the complex number system. 
A)    has degree 0 so there are no solutions in the complex number system. 
B)    has degree 4 so there are four solutions in the complex number system. 
C)    has degree 2 so there are two solutions in the complex number system. 
D)    has degree   so there are four solutions in the complex number system. 
E)    has degree -4 so there are no solutions in the complex number system.

Question 17

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 18

Write the following roots in standard form.(Round your answer to four decimal places.) ​
Cube roots of   ​

Accepted Answer

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

Question 19

Simplify the complex number and write it in standard form. ​   ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​8i 
A) ​   
B) ​   
C) ​   
D) ​   
E) ​8i

Question 20

Write the following roots in standard form.(Round your answer to four decimal places.) ​
Cube roots of   ​

Accepted Answer

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

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 the indicated roots of the complex number. Cube roots of

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

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

Solve the equation and write complex solutions in standard form.

Find the absolute value of the complex number 5 + 3i.

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

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

Represent the complex number graphically, and find the trigonometric form of the number. -8i

Perform the indicated operation in trigonometric form.Write the solution in standard form rounded to four decimal places.

Find all the zeros of the function and write the polynomial as a product of linear factors.

Solve the equation and write complex solutions in standard form.

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

Find a polynomial function with real coefficients that has the given zeros.

Determine the number of solutions of the equation in the complex number system.

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

Write the following roots in standard form.(Round your answer to four decimal places.) Cube roots of

Simplify the complex number and write it in standard form.

Write the following roots in standard form.(Round your answer to four decimal places.) Cube roots of

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Exam 4: Complex-Numbers

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 the indicated roots of the complex number. ​ Cube roots of ​

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

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

Solve the equation and write complex solutions in standard form. ​ ​

​Find the absolute value of the complex number 5 + 3i. ​

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

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

Represent the complex number graphically, and find the trigonometric form of the number. ​ -8i ​

Perform the indicated operation in trigonometric form.Write the solution in standard form rounded to four decimal places. ​

Find all the zeros of the function and write the polynomial as a product of linear factors. ​ ​

Solve the equation and write complex solutions in standard form. ​ ​ ​

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

Find a polynomial function with real coefficients that has the given zeros. ​ ​

Determine the number of solutions of the equation in the complex number system. ​ ​

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

Write the following roots in standard form.(Round your answer to four decimal places.) ​ Cube roots of ​

Simplify the complex number and write it in standard form. ​ ​

Write the following roots in standard form.(Round your answer to four decimal places.) ​ Cube roots of ​

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

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

Solve the equation and write complex solutions in standard form.

Find the absolute value of the complex number 5 + 3i.

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

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

Represent the complex number graphically, and find the trigonometric form of the number. -8i

Perform the indicated operation in trigonometric form.Write the solution in standard form rounded to four decimal places.

Find all the zeros of the function and write the polynomial as a product of linear factors.

Solve the equation and write complex solutions in standard form.

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

Find a polynomial function with real coefficients that has the given zeros.

Determine the number of solutions of the equation in the complex number system.

Write the following roots in standard form.(Round your answer to four decimal places.) Cube roots of

Simplify the complex number and write it in standard form.

Write the following roots in standard form.(Round your answer to four decimal places.) Cube roots of