Question 1

Find all solutions to the following equation.   ​

Accepted Answer

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

Question 2

Find the standard form of the complex number   . ​

Accepted Answer

A) ​8   - 8i 
B) ​-4   + 4i 
C) ​4   - 4i 
D) ​-8   + 8i 
E) ​4 + 4   i 
A) ​8   - 8i 
B) ​-4   + 4i 
C) ​4   - 4i 
D) ​-8   + 8i 
E) ​4 + 4   i

Question 3

Write the complex number in trigonometric form. ​   ​

Accepted Answer

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

Question 4

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate. ​   ​

Accepted Answer

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

Question 5

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 6

Find all zeros of the function f(x)=(x - 5)(x + 2)[x+(5 + 2i)][x-(5 - 2i)] ​

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

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 9

Use the formula to find one solution of the equation ​   ​

Accepted Answer

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

Question 10

Find the cube roots of the following complex number.Write each of the roots in standard form. -729

Accepted Answer

A)    
B)    
C)    
D) -9 
E)    
A)    
B)    
C)    
D) -9 
E)

Question 11

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 12

Given -6i is a root, determine all other roots of f(x)=x3 - 2x2 + 36x - 72. ​

Accepted Answer

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

Question 13

​Find the trigonometric form of the complex number shown below. ​
-7 - i

Accepted Answer

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

Question 14

Write the complex number in standard form.

Accepted Answer

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

Question 15

Perform the indicated operation using the standard form. ​   ​

Accepted Answer

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

Find all solutions to the following equation.

Find the standard form of the complex number .

Write the complex number in trigonometric form.

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate.

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

Find all zeros of the function f(x)=(x - 5)(x + 2)[x+(5 + 2i)][x-(5 - 2i)]

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

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

Use the formula to find one solution of the equation

Find the cube roots of the following complex number.Write each of the roots in standard form. -729

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

Given -6i is a root, determine all other roots of f(x)=x³ - 2x² + 36x - 72.

Find the trigonometric form of the complex number shown below. -7 - i

Write the complex number in standard form.

Perform the indicated operation using the standard form.

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Exam 4: Complex-Numbers

Find all solutions to the following equation. ​

Find the standard form of the complex number . ​

Write the complex number in trigonometric form. ​ ​

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate. ​ ​

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

Find all zeros of the function f(x)=(x - 5)(x + 2)[x+(5 + 2i)][x-(5 - 2i)] ​

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

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

Use the formula to find one solution of the equation ​ ​

Find the cube roots of the following complex number.Write each of the roots in standard form. -729

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

Given -6i is a root, determine all other roots of f(x)=x3 - 2x2 + 36x - 72. ​

​Find the trigonometric form of the complex number shown below. ​ -7 - i

Write the complex number in standard form.

Perform the indicated operation using the standard form. ​ ​

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Find all solutions to the following equation.

Find the standard form of the complex number .

Write the complex number in trigonometric form.

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate.

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

Find all zeros of the function f(x)=(x - 5)(x + 2)[x+(5 + 2i)][x-(5 - 2i)]

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

Use the formula to find one solution of the equation

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

Given -6i is a root, determine all other roots of f(x)=x³ - 2x² + 36x - 72.

Find the trigonometric form of the complex number shown below. -7 - i

Perform the indicated operation using the standard form.