Question 1

Show that   is a solution to the equation  .

Accepted Answer

Let's substitute   into the equation and simplify: ​  ​ 
Thus,   is a solution to the equation.

Question 2

Find three cube roots for the complex number. Leave your answers in trigonometric form.  ​

Accepted Answer

A)   
B)   
C)   
D)   
E)    D

Question 3

Solve the equation.  ​

Accepted Answer

A)   
B)   
C)   
D)   
E)    B

Question 4

Find all x and y between 0 and   so that the equation is true. ​  ​

Accepted Answer

A)   
B)  ​ 
C)  ​ 
D)  ​ 
E)  ​

Question 5

Simplify the power of i . ​  ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 6

Find the quotient   in standard form.  ,   ​

Accepted Answer

A)   
B)  ​ 
C)  ​ 
D)  ​ 
E)  ​

Question 7

Find three cube roots for the complex number. Leave your answers in trigonometric form.  ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 8

Write the complex number in standard form.  ​

Accepted Answer

A)   
B)  ​ 
C)  ​ 
D)  ​ 
E)  ​

Question 9

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

Accepted Answer

The answer of Use DeMoivre's Theorem to find the following....

Question 10

Graph the ordered pair on a polar coordinate system.  ​

Accepted Answer

A)  ​ 
B)  ​ 
C)  ​ 
D)  ​

Question 11

Graph the number along with its opposite and conjugate.  ​

Accepted Answer

A)  ​ 
B)  ​ 
C)  ​ 
D)  ​ 
E)  ​

Question 12

Solve the equation.

Accepted Answer

The answer of Solve the equation. ...

Question 13

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

Accepted Answer

A)  ​ 
B)  ​ 
C)   
D)  ​ 
E)  ​

Question 14

Convert the equation to polar coordinates and then sketch the graph. ​  ​

Accepted Answer

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

Question 15

Write the equation with rectangular coordinates.  ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 16

Find the product.

Accepted Answer

The answer of Find the product. ...

Question 17

Multiply. Leave the answer in trigonometric form.    ​

Accepted Answer

A)  ​ 
B)   
C)  ​ 
D)  ​ 
E)  ​

Question 18

Let   and   and find  .

Accepted Answer

The answer of Let   and   and find ...

Question 19

Convert to polar coordinates with  and  between  and  .  ​  ​

Accepted Answer

The answer of Convert to polar coordinates with  and...

Question 20

Find the product.

Accepted Answer

The answer of Find the product. ...

Exam 8: Complex Numbers and Polar Coordinates

Show that is a solution to the equation .

Find three cube roots for the complex number. Leave your answers in trigonometric form. ​

Solve the equation. ​

Find all x and y between 0 and so that the equation is true. ​ ​

Simplify the power of i . ​ ​

Find the quotient in standard form. , ​

Find three cube roots for the complex number. Leave your answers in trigonometric form. ​

Write the complex number in standard form. ​

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

Graph the ordered pair on a polar coordinate system. ​

Graph the number along with its opposite and conjugate. ​

Solve the equation.

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

Convert the equation to polar coordinates and then sketch the graph. ​ ​

Write the equation with rectangular coordinates. ​

Find the product.

Multiply. Leave the answer in trigonometric form. ​

Let and and find .

Convert to polar coordinates with and between and . ​ ​

Find the product.

Find three cube roots for the complex number. Leave your answers in trigonometric form.

Solve the equation.

Find all x and y between 0 and so that the equation is true.

Simplify the power of i .

Find the quotient in standard form. ,

Find three cube roots for the complex number. Leave your answers in trigonometric form.

Write the complex number in standard form.

Graph the ordered pair on a polar coordinate system.

Graph the number along with its opposite and conjugate.

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

Convert the equation to polar coordinates and then sketch the graph.

Write the equation with rectangular coordinates.

Multiply. Leave the answer in trigonometric form.

Convert to polar coordinates with and between and .