Question 1

Find real numbers a and b such that the equation is true. ​   ​

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

Represent the following complex number graphically. ​
​     ​
​

Accepted Answer

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

Question 4

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

Accepted Answer

A) 9.66 - 2.59i 
B) ​8.66 + 5i 
C) ​-9.66 - 2.59i 
D) ​-8.66 - 5i 
E) ​9.66 + 2.59i 
A) 9.66 - 2.59i 
B) ​8.66 + 5i 
C) ​-9.66 - 2.59i 
D) ​-8.66 - 5i 
E) ​9.66 + 2.59i

Question 5

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

Accepted Answer

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

Question 6

Use DeMoivre's Theorem to find the indicated power of the complex number.Write the result in standard form.(Round your answer to four decimal places.) ​   ​

Accepted Answer

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

Question 7

Perform the operation and leave the result in trigonometric form. ​   ​

Accepted Answer

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

Question 8

Write the complex number in standard 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)    
B)    
C)    
D)    
E) ​   
A)    
B)    
C)    
D)    
E) ​

Question 10

Use the given zero 2i to find all the zeros of the function. ​   ​

Accepted Answer

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

Question 11

Find a cubic polynomial function f with real coefficients that has zeros -2 + 5i and -2 - 5i and has x-intercept (0, 9]. ​

Accepted Answer

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

Question 12

Solve the equation.Write complex solutions in standard form. ​   ​

Accepted Answer

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

Question 13

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

Accepted Answer

A) The zeros of f(x) are x =   ,     
B) The zeros of f(x) are x = ±   ,     
C) The zeros of f(x) are x =   ,     
D) The zeros of f(x) are x = ±   ,     
E) The zeros of f(x) are x = -   ,     
A) The zeros of f(x) are x =   ,     
B) The zeros of f(x) are x = ±   ,     
C) The zeros of f(x) are x =   ,     
D) The zeros of f(x) are x = ±   ,     
E) The zeros of f(x) are x = -   ,

Question 14

Perform the operation and leave the result in trigonometric form. ​   ​

Accepted Answer

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

Question 15

Perform the operation and leave the result in trigonometric form. ​   ​

Accepted Answer

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

Question 16

Find the fourth-degree polynomial function f with real coefficients that has the zeros x=   i and x=-   i and the x- and y-intercepts shown in the graph. ​

Accepted Answer

A) ​   
B) f (x) = x4 + x3 + x - 8 
C) f (x) =   x4 +   x3 +   x - 8 
D) f (x) =   x4 +   x3 +   x - 8 
E) f (x) = 2x4 + 2x3 + 4x - 8 
A) ​   
B) f (x) = x4 + x3 + x - 8 
C) f (x) =   x4 +   x3 +   x - 8 
D) f (x) =   x4 +   x3 +   x - 8 
E) f (x) = 2x4 + 2x3 + 4x - 8

Question 17

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 18

Represent the complex number graphically, and find the trigonometric form of the number. ​
4
​

Accepted Answer

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

Question 19

Find a cubic polynomial function f with real coefficients that has zeros -4 and -2+   i where f(3) = -378. ​

Accepted Answer

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

Question 20

Write the complex number shown below in trigonometric form.

Accepted Answer

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

Find real numbers a and b such that the equation is true.

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

Represent the following complex number graphically.

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

Simplify the complex number and write it in standard form.

Use DeMoivre's Theorem to find the indicated power of the complex number.Write the result in standard form.(Round your answer to four decimal places.)

Perform the operation and leave the result in trigonometric form.

Write the complex number in standard form.

Find the trigonometric form of the complex number shown below.

Use the given zero 2i to find all the zeros of the function.

Find a cubic polynomial function f with real coefficients that has zeros -2 + 5i and -2 - 5i and has x-intercept (0, 9].

Solve the equation.Write complex solutions in standard form.

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

Perform the operation and leave the result in trigonometric form.

Perform the operation and leave the result in trigonometric form.

Find the fourth-degree polynomial function f with real coefficients that has the zeros x= i and x=- i and the x- and y-intercepts shown in the graph.

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

Represent the complex number graphically, and find the trigonometric form of the number. 4

Find a cubic polynomial function f with real coefficients that has zeros -4 and -2+ i where f(3) = -378.

Write the complex number shown below in trigonometric form.

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Exam 4: Complex-Numbers

Find real numbers a and b such that the equation is true. ​ ​

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

Represent the following complex number graphically. ​ ​ ​ ​

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

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

Use DeMoivre's Theorem to find the indicated power of the complex number.Write the result in standard form.(Round your answer to four decimal places.) ​ ​

Perform the operation and leave the result in trigonometric form. ​ ​

Write the complex number in standard form. ​ ​

Find the trigonometric form of the complex number shown below.

Use the given zero 2i to find all the zeros of the function. ​ ​

Find a cubic polynomial function f with real coefficients that has zeros -2 + 5i and -2 - 5i and has x-intercept (0, 9]. ​

Solve the equation.Write complex solutions in standard form. ​ ​

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

Perform the operation and leave the result in trigonometric form. ​ ​

Perform the operation and leave the result in trigonometric form. ​ ​

Find the fourth-degree polynomial function f with real coefficients that has the zeros x= i and x=- i and the x- and y-intercepts shown in the graph. ​

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

Represent the complex number graphically, and find the trigonometric form of the number. ​ 4 ​

Find a cubic polynomial function f with real coefficients that has zeros -4 and -2+ i where f(3) = -378. ​

Write the complex number shown below in trigonometric form.

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Find real numbers a and b such that the equation is true.

Represent the following complex number graphically.

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

Simplify the complex number and write it in standard form.

Use DeMoivre's Theorem to find the indicated power of the complex number.Write the result in standard form.(Round your answer to four decimal places.)

Perform the operation and leave the result in trigonometric form.

Write the complex number in standard form.

Use the given zero 2i to find all the zeros of the function.

Find a cubic polynomial function f with real coefficients that has zeros -2 + 5i and -2 - 5i and has x-intercept (0, 9].

Solve the equation.Write complex solutions in standard form.

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

Perform the operation and leave the result in trigonometric form.

Perform the operation and leave the result in trigonometric form.

Find the fourth-degree polynomial function f with real coefficients that has the zeros x= i and x=- i and the x- and y-intercepts shown in the graph.

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

Represent the complex number graphically, and find the trigonometric form of the number. 4

Find a cubic polynomial function f with real coefficients that has zeros -4 and -2+ i where f(3) = -378.