Question 1

Sketch the graph of the equation by making a table using values of θ  that are multiples of 45°.   ​

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Question 2

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 3

Convert to polar coordinates with   and   between   and   .   ​

Accepted Answer

The answer of Convert to polar coordinates with  ...

Question 4

For the ordered pair, give three other ordered pairs with degree values between   and   that name the same point.   ​

Accepted Answer

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Question 5

Graph the equation.   ​

Accepted Answer

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Question 6

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

Accepted Answer

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B) ​   
C) ​   
D) ​ ​   
E) ​   
A) ​ ​ ​   
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C) ​   
D) ​ ​   
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Question 7

Find two square roots for the complex number. Leave your answers in trigonometric form. ​   ​
Choose the correctly sketched graph of the two roots.
​

Accepted Answer

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B) ​   
C) ​   
D) ​   
E) ​   
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E) ​

Question 8

Use your graphing calculator to convert to polar coordinates. Round all values to four significant digits.   ​

Accepted Answer

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Question 9

Let    and    and find   . ​

Accepted Answer

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Question 10

Convert to polar coordinates with   and    between   and   .   ​

Accepted Answer

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Question 11

Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​   ​

Accepted Answer

A) ​64 
B) ​-16    + 16 ​i 
C) ​-8111 i ​1 
D) ​-16   + 16 ​i ​1 
E) ​-8 - 8 i ​   
A) ​64 
B) ​-16    + 16 ​i 
C) ​-8111 i ​1 
D) ​-16   + 16 ​i ​1 
E) ​-8 - 8 i ​

Question 12

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

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

Question 13

Divide. Leave your answer in trigonometric form.

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

Write the expression    in terms of i and then simplify.

Accepted Answer

The answer of Write the expression    in terms...

Question 16

Read the method of solving the system of equations.​ ​   ​
Solving the first equation for y , we have   . Substituting this value of y into the second equation, we have ​   ​
The equation is quadratic. We write it in standard form and apply the quadratic formula.   ​   ​                   ​   ​
Use the method shown above to solve the system of equations.   ​

Accepted Answer

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

Question 17

Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​   ​

Accepted Answer

A) ​-8 - 8 ​i ​   
B) ​1 8 i 1 1 1 1 11 
C) ​-​16 - 16 i   
D) ​116    + 16 i ​1 
E) ​8111 1 ​1 
A) ​-8 - 8 ​i ​   
B) ​1 8 i 1 1 1 1 11 
C) ​-​16 - 16 i   
D) ​116    + 16 i ​1 
E) ​8111 1 ​1

Question 18

Graph the equation.   ​

Accepted Answer

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

Question 19

Convert to polar coordinates with   and   between   and   ​(-41, -4   )​   ​

Accepted Answer

The answer of Convert to polar coordinates with  ...

Question 20

Change the equation to rectangular coordinates and then graph. ​   ​

Accepted Answer

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

Sketch the graph of the equation by making a table using values of θ that are multiples of 45°.

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

Convert to polar coordinates with and between and .

For the ordered pair, give three other ordered pairs with degree values between and that name the same point.

Graph the equation.

Graph the equation using your graphing calculator in polar mode.

Find two square roots for the complex number. Leave your answers in trigonometric form. Choose the correctly sketched graph of the two roots.

Use your graphing calculator to convert to polar coordinates. Round all values to four significant digits.

Let and and find .

Convert to polar coordinates with and between and .

Use DeMoivre's Theorem to find the following. Write your answer in standard form.

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.

Divide. Leave your answer in trigonometric form.

Graph the equation using your graphing calculator in polar mode.

Write the expression in terms of i and then simplify.

Use DeMoivre's Theorem to find the following. Write your answer in standard form.

Graph the equation.

Convert to polar coordinates with and between and (-41, -4 )

Change the equation to rectangular coordinates and then graph.

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

Sketch the graph of the equation by making a table using values of θ that are multiples of 45°. ​

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

Convert to polar coordinates with and between and . ​

For the ordered pair, give three other ordered pairs with degree values between and that name the same point. ​

Graph the equation. ​

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

Find two square roots for the complex number. Leave your answers in trigonometric form. ​ ​ Choose the correctly sketched graph of the two roots. ​

Use your graphing calculator to convert to polar coordinates. Round all values to four significant digits. ​

Let and and find . ​

Convert to polar coordinates with and between and . ​

Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​ ​

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. ​ ​

Divide. Leave your answer in trigonometric form.

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

Write the expression in terms of i and then simplify.

Use DeMoivre's Theorem to find the following. Write your answer in standard form. ​ ​

Graph the equation. ​

Convert to polar coordinates with and between and ​(-41, -4 )​ ​

Change the equation to rectangular coordinates and then graph. ​ ​

The Six Trigonometric Functions

Right Triangle Trigonometry

Radian Measure

Graphing and Inverse Functions

Identities and Formulas

Equations

Triangles

Filters

Sketch the graph of the equation by making a table using values of θ that are multiples of 45°.

Convert to polar coordinates with and between and .

For the ordered pair, give three other ordered pairs with degree values between and that name the same point.

Graph the equation.

Graph the equation using your graphing calculator in polar mode.

Find two square roots for the complex number. Leave your answers in trigonometric form. Choose the correctly sketched graph of the two roots.

Use your graphing calculator to convert to polar coordinates. Round all values to four significant digits.

Let and and find .

Convert to polar coordinates with and between and .

Use DeMoivre's Theorem to find the following. Write your answer in standard form.

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 equation using your graphing calculator in polar mode.

Use DeMoivre's Theorem to find the following. Write your answer in standard form.

Graph the equation.

Convert to polar coordinates with and between and (-41, -4 )

Change the equation to rectangular coordinates and then graph.