Question 1

Graph the equation. r = 5
​

Accepted Answer

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

Question 2

DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is   , which can be expressed as   Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below.

Accepted Answer

The answer of DeMoivre's Theorem can be used to find...

Question 3

Graph the ordered pair on a polar coordinate system.   ​

Accepted Answer

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

Question 4

Find the product    in standard form.   ​

Accepted Answer

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

Question 5

Find the quotient. Write the answer in standard form for complex numbers.

Accepted Answer

The answer of Find the quotient. Write the answer in...

Question 6

Find two square roots for the complex number. Write your answer in standard form.

Accepted Answer

The answer of Find two square roots for the complex...

Question 7

Is    a solution to the equation   ? ​

Accepted Answer

A) no 
B) yes 
A) no 
B) yes

Question 8

Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.   ​

Accepted Answer

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

Question 9

Convert to rectangular coordinates. Use exact values.   ​

Accepted Answer

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

Question 10

Graph the equation using your graphing calculator in polar mode.   ​

Accepted Answer

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

Question 11

Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .   ​

Accepted Answer

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

Question 12

Write    and    in trigonometric form and find their product. ​   ​

Accepted Answer

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

Question 13

Find two square roots for the complex number. Write your answer in standard form.   ​

Accepted Answer

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

Question 14

Write    and    in trigonometric form and then find their quotient. ​   ​

Accepted Answer

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

Question 15

Find x and y (real numbers)so that the equation is true.   ​

Accepted Answer

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

Question 16

Let    and    and find   .

Accepted Answer

The answer of Let    and    and...

Question 17

Combine the complex numbers.   ​

Accepted Answer

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

Question 18

Solve the equation. Leave your solution in trigonometric form.   ​

Accepted Answer

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

Question 19

Combine the complex numbers.

Accepted Answer

The answer of Combine the complex numbers.  ...

Question 20

Divide. Leave your answer in trigonometric form.

Accepted Answer

The answer of Divide. Leave your answer in trigonometric form....

Graph the equation. r = 5

DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is , which can be expressed as Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below.

Graph the ordered pair on a polar coordinate system.

Find the product in standard form.

Find the quotient. Write the answer in standard form for complex numbers.

Find two square roots for the complex number. Write your answer in standard form.

Is a solution to the equation ?

Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.

Convert to rectangular coordinates. Use exact values.

Graph the equation using your graphing calculator in polar mode.

Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .

Write and in trigonometric form and find their product.

Find two square roots for the complex number. Write your answer in standard form.

Write and in trigonometric form and then find their quotient.

Find x and y (real numbers)so that the equation is true.

Let and and find .

Combine the complex numbers.

Solve the equation. Leave your solution in trigonometric form.

Combine the complex numbers.

Divide. Leave your answer in trigonometric form.

The Six Trigonometric Functions

Right Triangle Trigonometry

Radian Measure

Graphing and Inverse Functions

Identities and Formulas

Equations

Triangles

Filters

Exam 8: Complex Numbers and Polar Coordinates

Graph the equation. r = 5 ​

DeMoivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of x is , which can be expressed as Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below.

Graph the ordered pair on a polar coordinate system. ​

Find the product in standard form. ​

Find the quotient. Write the answer in standard form for complex numbers.

Find two square roots for the complex number. Write your answer in standard form.

Is a solution to the equation ? ​

Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree. ​

Convert to rectangular coordinates. Use exact values. ​

Graph the equation using your graphing calculator in polar mode. ​

Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ . ​

Write and in trigonometric form and find their product. ​ ​

Find two square roots for the complex number. Write your answer in standard form. ​

Write and in trigonometric form and then find their quotient. ​ ​

Find x and y (real numbers)so that the equation is true. ​

Let and and find .

Combine the complex numbers. ​

Solve the equation. Leave your solution in trigonometric form. ​

Combine the complex numbers.

Divide. Leave your answer in trigonometric form.

The Six Trigonometric Functions

Right Triangle Trigonometry

Radian Measure

Graphing and Inverse Functions

Identities and Formulas

Equations

Triangles

Filters

Graph the equation. r = 5

Graph the ordered pair on a polar coordinate system.

Find the product in standard form.

Is a solution to the equation ?

Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.

Convert to rectangular coordinates. Use exact values.

Graph the equation using your graphing calculator in polar mode.

Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .

Write and in trigonometric form and find their product.

Find two square roots for the complex number. Write your answer in standard form.

Write and in trigonometric form and then find their quotient.

Find x and y (real numbers)so that the equation is true.

Combine the complex numbers.

Solve the equation. Leave your solution in trigonometric form.