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Deck 8: Complex Numbers and Polar Coordinates
Full screen (f)
Question
Combine the complex numbers. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the product. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the product. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Is 
a solution to the equation 
?
A)no
B)yes
a solution to the equation ? A)no
B)yes
Question
Let 
and 
and find 
.
A)
B)
C)
D)
E)
and and find . A)
B)
C)
D)
E)
Question
Let 
and 
and find 
.
A)
B)
C)
D)
E)
and and find . A)
B)
C)
D)
E)
Question
Combine the complex numbers. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Write the expression 
in terms of i.
A)
B)
C)
D)
E)
in terms of i.A)
B)
C)
D)
E)
Question
Simplify the power of i . 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find x and y (real numbers)so that the equation is true. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Question
Let 
and 
and find 
. 
and and find . Question
Find the product. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the product. 
Question
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.
A)
B)
C)
D)
E)
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.
A)
B)
C)
D)
E)
Question
Find the quotient. Write the answer in standard form for complex numbers. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Write the expression 
in terms of i and then simplify.
A)
B)
C)
D)
E)
in terms of i and then simplify. A)
B)
C)
D)
E)
Question
Find all x and y between 0 and 
so that the equation is true. 
A)
B)
C)
D)
E)
so that the equation is true. A)
B)
C)
D)
E)
Question
Write the expression 
in terms of i and then simplify.
in terms of i and then simplify. Question
Write the expression 
in terms of i .
in terms of i . Question
Graph the complex number and give the absolute value of the number. 
A)
B)
C)
D) 
E)
A)
B)
C)
D)
E)
Question
Show that 
is a solution to the equation 
.
is a solution to the equation . Question
Combine the complex numbers. 
Question
Combine the complex numbers. 
Question
Graph the number along with its opposite and conjugate. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the quotient. Write the answer in standard form for complex numbers. 
Question
Find the product. 
Question
Write the complex number in standard form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Let 
and 
and find 
. 
and and find . Question
Write the complex number in standard form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Simplify the power of i . 
Question
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.
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.
Question
Graph the complex number and give the absolute value of it. 
A)
The absolute value is 11
B)
The absolute value is 14
C)
The absolute value is 11
D) 
The absolute value is 10
E)
The absolute value is 14
A)
The absolute value is 11
B)
The absolute value is 14
C)
The absolute value is 11
D)
The absolute value is 10
E)
The absolute value is 14
Question
Graph the complex number along with its opposite and conjugate. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Question
Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Graph the complex number along with its opposite and conjugate. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the product. 
Question
Find x and y (real numbers)so that the equation is true. 
Question
Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree. 
Question
Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ . 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree. 
Question
Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree. 
Question
Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ . 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree. 
Question
Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree. 
Question
Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ . 
Question
Write the complex number in standard form. 
Question
Write the complex number in standard form. 
Question
Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ . 
Question
Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ . 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree. 
Question
Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ . 
Question
Convert complex numbers to trigonometric form and then simplify the expression. Write the answer in standard form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use DeMoivre's Theorem to find the following. Write your answer in standard form. 
Question
Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth. 
Question
Use DeMoivre's Theorem to find the following. Write your answer in standard form. 
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 1E)8111 1 1
Question
Multiply. Leave the answer in trigonometric form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use DeMoivre's Theorem to find the following. Write your answer in standard form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
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. 
A)
B)
C)
D)
E)
, which can be expressed as Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. A)
B)
C)
D)
E)
Question
Use DeMoivre's Theorem to find the following. Write your answer in standard form. 
A)64
B)-16
+ 16 i
C)-8111 i 1
D)-16
+ 16 i 1
E)-8 - 8 i 
A)64
B)-16
+ 16 iC)-8111 i 1
D)-16
+ 16 i 1E)-8 - 8 i
Question
Write 
and 
in trigonometric form and find their product. 
A)
B)
C)
D)
E)
and in trigonometric form and find their product. A)
B)
C)
D)
E)
Question
Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth. 
Question
Use DeMoivre's Theorem to find the following. Write your answer in standard form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Divide. Leave your answer in trigonometric form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the quotient 
in standard form. 
, 
A)
B)
C)
D)
E)
in standard form. , A)
B)
C)
D)
E)
Question
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. 
A)
B)
C)
D)
E)
, which can be expressed as Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. A)
B)
C)
D)
E)
Question
Find the product 
in standard form. 
A)
B)
C)
D)
E)
in standard form. A)
B)
C)
D)
E)
Question
Divide. Leave your answer in trigonometric form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Multiply. Leave the answer in trigonometric form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Multiply. Leave the answer in trigonometric form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Write 
and 
in trigonometric form and find their product. 
A)
B)
C)
D)
E)
and in trigonometric form and find their product. A)
B)
C)
D)
E)
Question
Write 
and 
in trigonometric form and then find their quotient. 
A)
B)
C)
D)
E)
and in trigonometric form and then find their quotient. A)
B)
C)
D)
E)
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Full screen (f)
Deck 8: Complex Numbers and Polar Coordinates
1
Combine the complex numbers.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
2
Find the product.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
3
Find the product.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
4
Is a solution to the equation ?
A)no
B)yes
a solution to the equation ? A)no
B)yes
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5
Let and and find .
A)
B)
C)
D)
E)
and and find . A)
B)
C)
D)
E)
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6
Let and and find .
A)
B)
C)
D)
E)
and and find . A)
B)
C)
D)
E)
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7
Combine the complex numbers.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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8
Write the expression in terms of i.
A)
B)
C)
D)
E)
in terms of i.A)
B)
C)
D)
E)
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9
Simplify the power of i .
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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10
Find x and y (real numbers)so that the equation is true.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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11
If z is a complex number then the product of z and its conjugate is a real number.
A)false
B)true
A)false
B)true
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12
Let and and find .
and and find . Unlock Deck
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13
Find the product.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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14
Find the product.
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15
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.
A)
B)
C)
D)
E)
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.
A)
B)
C)
D)
E)
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16
Find the quotient. Write the answer in standard form for complex numbers.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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17
Write the expression in terms of i and then simplify.
A)
B)
C)
D)
E)
in terms of i and then simplify. A)
B)
C)
D)
E)
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18
Find all x and y between 0 and so that the equation is true.
A)
B)
C)
D)
E)
so that the equation is true. A)
B)
C)
D)
E)
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19
Write the expression in terms of i and then simplify.
in terms of i and then simplify. Unlock Deck
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20
Write the expression in terms of i .
in terms of i . Unlock Deck
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21
Graph the complex number and give the absolute value of the number.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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22
Show that is a solution to the equation .
is a solution to the equation . Unlock Deck
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23
Combine the complex numbers.
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24
Combine the complex numbers.
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25
Graph the number along with its opposite and conjugate.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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26
Find the quotient. Write the answer in standard form for complex numbers.
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27
Find the product.
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28
Write the complex number in standard form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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29
Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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30
Let and and find .
and and find . Unlock Deck
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31
Write the complex number in standard form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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32
Simplify the power of i .
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33
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.
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.
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34
Graph the complex number and give the absolute value of it.
A)
The absolute value is 11
B)
The absolute value is 14
C)
The absolute value is 11
D)
The absolute value is 10
E)
The absolute value is 14
A)
The absolute value is 11
B)
The absolute value is 14
C)
The absolute value is 11
D)
The absolute value is 10
E)
The absolute value is 14
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35
Graph the complex number along with its opposite and conjugate.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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36
If z is a complex number, show that the sum of z and its conjugate is a real number.
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37
Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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38
Graph the complex number along with its opposite and conjugate.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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39
Find the product.
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40
Find x and y (real numbers)so that the equation is true.
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41
Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.
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42
Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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43
Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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44
Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.
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45
Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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46
Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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47
Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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48
Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.
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49
Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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50
Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.
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51
Use your graphing calculator to convert the complex number to trigonometric form. Round the angle to the nearest hundredth of a degree.
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52
Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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53
Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .
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54
Write the complex number in standard form.
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55
Write the complex number in standard form.
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56
Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .
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k this deck
57
Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 177 flashcards in this deck.
Unlock Deck
k this deck
58
Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 177 flashcards in this deck.
Unlock Deck
k this deck
59
Write the complex number in trigonometric form. Round the angle to the nearest hundredth of a degree.
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k this deck
60
Write the complex number in trigonometric form. Begin by sketching the graph to help find the argument θ .
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k this deck
61
Convert complex numbers to trigonometric form and then simplify the expression. Write the answer in standard form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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62
Use DeMoivre's Theorem to find the following. Write your answer in standard form.
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63
Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth.
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64
Use DeMoivre's Theorem to find the following. Write your answer in standard form.
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 1E)8111 1 1
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65
Multiply. Leave the answer in trigonometric form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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66
Use DeMoivre's Theorem to find the following. Write your answer in standard form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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k this deck
67
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.
A)
B)
C)
D)
E)
, which can be expressed as Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. A)
B)
C)
D)
E)
Unlock Deck
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68
Use DeMoivre's Theorem to find the following. Write your answer in standard form.
A)64
B)-16 + 16 i
C)-8111 i 1
D)-16 + 16 i 1
E)-8 - 8 i
A)64
B)-16
+ 16 iC)-8111 i 1
D)-16
+ 16 i 1E)-8 - 8 i
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69
Write and in trigonometric form and find their product.
A)
B)
C)
D)
E)
and in trigonometric form and find their product. A)
B)
C)
D)
E)
Unlock Deck
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70
Use a calculator to help write the complex number in standard form. Round the numbers in your answer to the nearest hundredth.
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71
Use DeMoivre's Theorem to find the following. Write your answer in standard form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 177 flashcards in this deck.
Unlock Deck
k this deck
72
Divide. Leave your answer in trigonometric form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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73
Find the quotient in standard form. ,
A)
B)
C)
D)
E)
in standard form. , A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 177 flashcards in this deck.
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k this deck
74
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.
A)
B)
C)
D)
E)
, which can be expressed as Use this fact, along with DeMoivre's Theorem, to find the reciprocal of the number below. A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 177 flashcards in this deck.
Unlock Deck
k this deck
75
Find the product in standard form.
A)
B)
C)
D)
E)
in standard form. A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 177 flashcards in this deck.
Unlock Deck
k this deck
76
Divide. Leave your answer in trigonometric form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
k this deck
77
Multiply. Leave the answer in trigonometric form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 177 flashcards in this deck.
Unlock Deck
k this deck
78
Multiply. Leave the answer in trigonometric form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 177 flashcards in this deck.
Unlock Deck
k this deck
79
Write and in trigonometric form and find their product.
A)
B)
C)
D)
E)
and in trigonometric form and find their product. A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 177 flashcards in this deck.
Unlock Deck
k this deck
80
Write and in trigonometric form and then find their quotient.
A)
B)
C)
D)
E)
and in trigonometric form and then find their quotient. A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 177 flashcards in this deck.
Unlock Deck
k this deck
Unlock Deck
Unlock for access to all 177 flashcards in this deck.
