Question 1

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 2

Find a cubic polynomial function f with real coefficients that has zeros 4 +   i and 4 -   i and has x-intercept [-2,0). ​

Accepted Answer

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

Question 3

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

Accepted Answer

A) ​a = 0, b = -   
B) ​​a = 0, b = -   
C) ​​a = 0, b = -   
D) ​​a = 0, b = -9 
E) ​​a = 0, b = -10 
A) ​a = 0, b = -   
B) ​​a = 0, b = -   
C) ​​a = 0, b = -   
D) ​​a = 0, b = -9 
E) ​​a = 0, b = -10

Question 4

Use the formula to find the missing quantity for the given conditions.The formula E=IZ where E represents voltage, I represents current, and Z represents impedance (a measure of opposition to a sinusoidal electric current), is used in electrical engineering.The variable is a complex number. ​   ​

Accepted Answer

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

Question 5

Write the complex number in standard form. ​   ​

Accepted Answer

A) (24 -   ) - (6   - 4   )i 
B) (24 +   ) + (6   - 4   )i 
C) (24 -   ) + (6   - 4   )i 
D) (24 +   ) - (6   - 4   )i 
E) (24 +   ) + (6   + 4   )i 
A) (24 -   ) - (6   - 4   )i 
B) (24 +   ) + (6   - 4   )i 
C) (24 -   ) + (6   - 4   )i 
D) (24 +   ) - (6   - 4   )i 
E) (24 +   ) + (6   + 4   )i

Question 6

Write the quotient in standard form. ​   ​

Accepted Answer

A) ​   
B) ​   
C) ​-2i 
D) ​   
E) ​2i 
A) ​   
B) ​   
C) ​-2i 
D) ​   
E) ​2i

Question 7

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

Accepted Answer

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

Question 8

Given 2+i is a root, determine all other roots of f(x)=​x5 - 6x4 + 15x3 - 18x2 + 10x. ​

Accepted Answer

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

Question 9

Write the quotient in standard form. ​   ​

Accepted Answer

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

Question 10

Find a polynomial with real coefficients that has zeros 3, 10i, and -10i. ​

Accepted Answer

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

Question 11

Use the formula to find the missing quantity for the given conditions.The formula E=IZ where E represents voltage, I represents current, and Z represents impedance (a measure of opposition to a sinusoidal electric current), is used in electrical engineering.The variable is a complex number. ​   ​

Accepted Answer

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

Question 12

Find all solutions to the following equation.

Accepted Answer

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

Question 13

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

Accepted Answer

A) cos 17° - isin 17° 
B) cos 31° - isin 31° 
C) cos 17° + isin 17° 
D) cos 31° + icos 31° 
E) cos 31° + isin 31° 
A) cos 17° - isin 17° 
B) cos 31° - isin 31° 
C) cos 17° + isin 17° 
D) cos 31° + icos 31° 
E) cos 31° + isin 31°

Question 14

Represent the complex number graphically, and find the trigonometric form of the number. ​
5 + 5i
​

Accepted Answer

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

Question 15

Find all solutions of ​x4 - 5x3+x - 5=0. ​

Accepted Answer

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

Question 16

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

Accepted Answer

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

Question 17

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 18

Write the complex number in standard form. ​   ​

Accepted Answer

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

Question 19

Plot the complex number and find its absolute value. ​
-3 + 9i
​

Accepted Answer

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

Question 20

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

Accepted Answer

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

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

Find a cubic polynomial function f with real coefficients that has zeros 4 + i and 4 - i and has x-intercept [-2,0).

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

Use the formula to find the missing quantity for the given conditions.The formula E=IZ where E represents voltage, I represents current, and Z represents impedance (a measure of opposition to a sinusoidal electric current), is used in electrical engineering.The variable is a complex number.

Write the complex number in standard form.

Write the quotient in standard form.

Solve the equation .Write complex solutions in standard form.

Given 2+i is a root, determine all other roots of f(x)=x⁵ - 6x⁴ + 15x³ - 18x² + 10x.

Write the quotient in standard form.

Find a polynomial with real coefficients that has zeros 3, 10i, and -10i.

Use the formula to find the missing quantity for the given conditions.The formula E=IZ where E represents voltage, I represents current, and Z represents impedance (a measure of opposition to a sinusoidal electric current), is used in electrical engineering.The variable is a complex number.

Find all solutions to the following equation.

Perform the operation and leave the result in trigonometric form.

Represent the complex number graphically, and find the trigonometric form of the number. 5 + 5i

Find all solutions of x⁴ - 5x³+x - 5=0.

Solve the equation .Write complex solutions in standard form.

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

Write the complex number in standard form.

Plot the complex number and find its absolute value. -3 + 9i

Simplify the complex number and write it in standard form.

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Exam 4: Complex-Numbers

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

Find a cubic polynomial function f with real coefficients that has zeros 4 + i and 4 - i and has x-intercept [-2,0). ​

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

Use the formula to find the missing quantity for the given conditions.The formula E=IZ where E represents voltage, I represents current, and Z represents impedance (a measure of opposition to a sinusoidal electric current), is used in electrical engineering.The variable is a complex number. ​ ​

Write the complex number in standard form. ​ ​

Write the quotient in standard form. ​ ​

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

Given 2+i is a root, determine all other roots of f(x)=​x5 - 6x4 + 15x3 - 18x2 + 10x. ​

Write the quotient in standard form. ​ ​

Find a polynomial with real coefficients that has zeros 3, 10i, and -10i. ​

Use the formula to find the missing quantity for the given conditions.The formula E=IZ where E represents voltage, I represents current, and Z represents impedance (a measure of opposition to a sinusoidal electric current), is used in electrical engineering.The variable is a complex number. ​ ​

Find all solutions to the following equation.

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

Represent the complex number graphically, and find the trigonometric form of the number. ​ 5 + 5i ​

Find all solutions of ​x4 - 5x3+x - 5=0. ​

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

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

Write the complex number in standard form. ​ ​

Plot the complex number and find its absolute value. ​ -3 + 9i ​

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

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

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

Find a cubic polynomial function f with real coefficients that has zeros 4 + i and 4 - i and has x-intercept [-2,0).

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

Use the formula to find the missing quantity for the given conditions.The formula E=IZ where E represents voltage, I represents current, and Z represents impedance (a measure of opposition to a sinusoidal electric current), is used in electrical engineering.The variable is a complex number.

Write the complex number in standard form.

Write the quotient in standard form.

Solve the equation .Write complex solutions in standard form.

Given 2+i is a root, determine all other roots of f(x)=x⁵ - 6x⁴ + 15x³ - 18x² + 10x.

Write the quotient in standard form.

Find a polynomial with real coefficients that has zeros 3, 10i, and -10i.

Use the formula to find the missing quantity for the given conditions.The formula E=IZ where E represents voltage, I represents current, and Z represents impedance (a measure of opposition to a sinusoidal electric current), is used in electrical engineering.The variable is a complex number.

Perform the operation and leave the result in trigonometric form.

Represent the complex number graphically, and find the trigonometric form of the number. 5 + 5i

Find all solutions of x⁴ - 5x³+x - 5=0.

Solve the equation .Write complex solutions in standard form.

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

Write the complex number in standard form.

Plot the complex number and find its absolute value. -3 + 9i

Simplify the complex number and write it in standard form.