Question 1

Find all solutions to the following equation. $x ^ { 3 } + 729 = 0$ ​

Accepted Answer

A)  $x = - 9$ 
B)  $x = 9 i , - \frac { 9 \sqrt { 3 } } { 2 } - \frac { 9 } { 2 } i , \frac { 9 \sqrt { 3 } } { 2 } - \frac { 9 } { 2 } i$ 
C)  $x = - 9 i$ 
D)  $x = 9 i , - \frac { 9 \sqrt { 3 } } { 2 } - \frac { 9 } { 2 } i , - \frac { 9 \sqrt { 3 } } { 2 } + \frac { 9 } { 2 } i$ 
E)  $x = - 9 i , - \frac { 9 \sqrt { 3 } } { 2 } - \frac { 9 } { 2 } i , - \frac { 9 \sqrt { 3 } } { 2 } + \frac { 9 } { 2 } i$ 
A)  $x = - 9$ 
B)  $x = 9 i , - \frac { 9 \sqrt { 3 } } { 2 } - \frac { 9 } { 2 } i , \frac { 9 \sqrt { 3 } } { 2 } - \frac { 9 } { 2 } i$ 
C)  $x = - 9 i$ 
D)  $x = 9 i , - \frac { 9 \sqrt { 3 } } { 2 } - \frac { 9 } { 2 } i , - \frac { 9 \sqrt { 3 } } { 2 } + \frac { 9 } { 2 } i$ 
E)  $x = - 9 i , - \frac { 9 \sqrt { 3 } } { 2 } - \frac { 9 } { 2 } i , - \frac { 9 \sqrt { 3 } } { 2 } + \frac { 9 } { 2 } i$

Question 2

Perform the indicated operation using trigonometric form.Leave answer in trigonometric form. $$( - 6 - 6 i ) ( - 5 - 5 i )$$

Accepted Answer

A)  $30 \left( \cos \frac { \pi } { 8 } + i \sin \frac { \pi } { 8 } \right)$ ​ 
B)  $- 60 \left( \cos \frac { \pi } { 8 } + i \sin \frac { \pi } { 8 } \right)$ ​ 
C)  $30 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$ ​ 
D)  $60 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$ ​ 
E)  $- 30 \left( \cos \frac { \pi } { 8 } + i \sin \frac { \pi } { 8 } \right)$ ​ 
A)  $30 \left( \cos \frac { \pi } { 8 } + i \sin \frac { \pi } { 8 } \right)$ ​ 
B)  $- 60 \left( \cos \frac { \pi } { 8 } + i \sin \frac { \pi } { 8 } \right)$ ​ 
C)  $30 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$ ​ 
D)  $60 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$ ​ 
E)  $- 30 \left( \cos \frac { \pi } { 8 } + i \sin \frac { \pi } { 8 } \right)$ ​

Question 3

Multiply the complex numbers.Write the answer in trigonometric form.​ $$9 \left( \cos \frac { 7 \pi } { 6 } + i \sin \frac { 7 \pi } { 6 } \right) 4 \left( \cos \frac { 3 \pi } { 7 } + i \sin \frac { 3 \pi } { 7 } \right)$$ ​

Accepted Answer

A)  $36 \left( \cos \frac { 67 \pi } { 42 } + i \sin \frac { 67 \pi } { 42 } \right)$ 
B)  $36 \left( \cos \frac { 10 \pi } { 13 } + i \sin \frac { 10 \pi } { 13 } \right)$ 
C) ​ $36 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$ 
D) ​ $13 \left( \cos \frac { 67 \pi } { 42 } + i \sin \frac { 67 \pi } { 42 } \right)$ 
E) ​ $13 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$ 
A)  $36 \left( \cos \frac { 67 \pi } { 42 } + i \sin \frac { 67 \pi } { 42 } \right)$ 
B)  $36 \left( \cos \frac { 10 \pi } { 13 } + i \sin \frac { 10 \pi } { 13 } \right)$ 
C) ​ $36 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$ 
D) ​ $13 \left( \cos \frac { 67 \pi } { 42 } + i \sin \frac { 67 \pi } { 42 } \right)$ 
E) ​ $13 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$

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.​ $\begin{array} { l } 
I = 8 + 2 i \
Z = 4 + 3 i
\end{array}$ ​

Accepted Answer

A)  $32 - 26 i$ 
B) ​ $32 + 26 i$ 
C) ​ $26 - 32 i$ 
D) ​ $26 - 26 i$ 
E) ​ $26 + 32 i$ 
A)  $32 - 26 i$ 
B) ​ $32 + 26 i$ 
C) ​ $26 - 32 i$ 
D) ​ $26 - 26 i$ 
E) ​ $26 + 32 i$

Question 5

Find the absolute value of the complex number -3 + 5i.

Accepted Answer

A)  $2 \sqrt { 2 }$ 
B) ​ $4 \sqrt { 34 }$ 
C) ​34 
D) ​ $\sqrt { 34 }$ 
E) ​ $4 \sqrt { 2 }$ 
A)  $2 \sqrt { 2 }$ 
B) ​ $4 \sqrt { 34 }$ 
C) ​34 
D) ​ $\sqrt { 34 }$ 
E) ​ $4 \sqrt { 2 }$

Question 6

Find the product $( 6 + 6 i ) ( 2 - 2 i )$ using trigonometric forms.Leave the result in trigonometric form.

Accepted Answer

A)  $12 \left( \cos \left( 45 ^ { \circ } \right) + i \sin \left( 45 ^ { \circ } \right) \right)$ 
B)  $12 \left( \cos \left( 0 ^ { \circ } \right) + i \sin \left( 0 ^ { \circ } \right) \right)$ 
C)  $24 \left( \cos \left( - 45 ^ { \circ } \right) + i \sin \left( - 45 ^ { \circ } \right) \right)$ 
D)  $24 \left( \cos \left( 45 ^ { \circ } \right) + i \sin \left( 45 ^ { \circ } \right) \right)$ 
E)  $24 \left( \cos \left( 0 ^ { \circ } \right) + i \sin \left( 0 ^ { \circ } \right) \right)$ 
A)  $12 \left( \cos \left( 45 ^ { \circ } \right) + i \sin \left( 45 ^ { \circ } \right) \right)$ 
B)  $12 \left( \cos \left( 0 ^ { \circ } \right) + i \sin \left( 0 ^ { \circ } \right) \right)$ 
C)  $24 \left( \cos \left( - 45 ^ { \circ } \right) + i \sin \left( - 45 ^ { \circ } \right) \right)$ 
D)  $24 \left( \cos \left( 45 ^ { \circ } \right) + i \sin \left( 45 ^ { \circ } \right) \right)$ 
E)  $24 \left( \cos \left( 0 ^ { \circ } \right) + i \sin \left( 0 ^ { \circ } \right) \right)$

Question 7

Perform the operation and leave the result in trigonometric form.​ $$\left( \cos 7 ^ { \circ } + i \sin 7 ^ { \circ } \right) \left( \cos 24 ^ { \circ } + i \sin 24 ^ { \circ } \right)$$ ​

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 8

Perform the indicated operation using the standard form.​ $$5 i ( 1 - \sqrt { 2 } i )$$ ​

Accepted Answer

A)  $5 i ( 1 - \sqrt { 2 } i ) \approx 7.07 + 5 i$ 
B) ​ $5 i ( 1 - \sqrt { 2 } i ) \approx 5 + 7.07 i$ 
C) ​ $5 i ( 1 - \sqrt { 2 } i ) \approx 1 + 5 \sqrt { 2 i }$ 
D) ​ $5 i ( 1 - \sqrt { 2 } i ) \approx 5 - 7.07 i$ 
E) ​ $5 i ( 1 - \sqrt { 2 } i ) \approx 7.07 - 5 i$ 
A)  $5 i ( 1 - \sqrt { 2 } i ) \approx 7.07 + 5 i$ 
B) ​ $5 i ( 1 - \sqrt { 2 } i ) \approx 5 + 7.07 i$ 
C) ​ $5 i ( 1 - \sqrt { 2 } i ) \approx 1 + 5 \sqrt { 2 i }$ 
D) ​ $5 i ( 1 - \sqrt { 2 } i ) \approx 5 - 7.07 i$ 
E) ​ $5 i ( 1 - \sqrt { 2 } i ) \approx 7.07 - 5 i$

Question 9

Represent the complex number below graphically. $$2 \left( \cos 135 ^ { \circ } + i \sin 135 ^ { \circ } \right)$$

Accepted Answer

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

Question 10

​Find the absolute value of the complex number 5 + 3i. ​

Accepted Answer

A) ​ $\sqrt { 34 }$ 
B) ​34 
C) ​ $$2 \sqrt { 34 }$$ 
D) ​5 + 3​i 
E) ​ $2 \sqrt { 2 }$ 
A) ​ $\sqrt { 34 }$ 
B) ​34 
C) ​ $$2 \sqrt { 34 }$$ 
D) ​5 + 3​i 
E) ​ $2 \sqrt { 2 }$

Question 11

Find the standard form of the complex number shown below.Round answers to two decimal places. $8 \left( \cos 245 ^ { \circ } + i \sin 245 ^ { \circ } \right)$

Accepted Answer

A)  $- 3.38 - 7.25 i$ 
B)  $- 3.61 - 7.64 i$ 
C)  $- 4.13 - 8.35 i$ 
D)  $- 4.62 - 8.60 i$ 
E)  $- 4.80 - 8.78 i$ 
A)  $- 3.38 - 7.25 i$ 
B)  $- 3.61 - 7.64 i$ 
C)  $- 4.13 - 8.35 i$ 
D)  $- 4.62 - 8.60 i$ 
E)  $- 4.80 - 8.78 i$

Question 12

Perform the operation and leave the result in trigonometric form.​ $$\frac { 16 \left( \cos 98 ^ { \circ } + i \sin 98 ^ { \circ } \right) } { 2 \left( \cos 128 ^ { \circ } + i \sin 128 ^ { \circ } \right) }$$ ​

Accepted Answer

A)  $8 \left( \cos 330 ^ { \circ } + i \sin 330 ^ { \circ } \right)$ 
B) ​ $8 \left( \cos 98 ^ { \circ } - i \sin 98 ^ { \circ } \right)$ 
C) ​ $8 \left( \cos 128 ^ { \circ } + i \sin 128 ^ { \circ } \right)$ 
D) ​ $8 \left( \cos 330 ^ { \circ } - i \sin 330 ^ { \circ } \right)$ 
E) ​ $8 \left( \cos 98 ^ { \circ } + i \sin 98 ^ { \circ } \right)$ 
A)  $8 \left( \cos 330 ^ { \circ } + i \sin 330 ^ { \circ } \right)$ 
B) ​ $8 \left( \cos 98 ^ { \circ } - i \sin 98 ^ { \circ } \right)$ 
C) ​ $8 \left( \cos 128 ^ { \circ } + i \sin 128 ^ { \circ } \right)$ 
D) ​ $8 \left( \cos 330 ^ { \circ } - i \sin 330 ^ { \circ } \right)$ 
E) ​ $8 \left( \cos 98 ^ { \circ } + i \sin 98 ^ { \circ } \right)$

Question 13

Perform the operation and leave the result in trigonometric form.​ $$\frac { \left( \cos 110 ^ { \circ } + i \sin 110 ^ { \circ } \right) } { 2 \left( \cos 50 ^ { \circ } + i \sin 50 ^ { \circ } \right) }$$ ​

Accepted Answer

A)  $\frac { 1 } { 2 } \left( \cos 60 ^ { \circ } + i \sin 60 ^ { \circ } \right)$ 
B) ​ $\frac { 1 } { 2 } \left( \cos 60 ^ { \circ } - i \sin 60 ^ { \circ } \right)$ 
C) ​ $\frac { 1 } { 2 } \left( \cos 110 ^ { \circ } + i \sin 110 ^ { \circ } \right)$ 
D) ​ $\frac { 1 } { 2 } \left( \cos 110 ^ { \circ } - i \sin 110 ^ { \circ } \right)$ 
E) ​ $\frac { 1 } { 2 } \left( \cos 50 ^ { \circ } + i \sin 50 ^ { \circ } \right)$ 
A)  $\frac { 1 } { 2 } \left( \cos 60 ^ { \circ } + i \sin 60 ^ { \circ } \right)$ 
B) ​ $\frac { 1 } { 2 } \left( \cos 60 ^ { \circ } - i \sin 60 ^ { \circ } \right)$ 
C) ​ $\frac { 1 } { 2 } \left( \cos 110 ^ { \circ } + i \sin 110 ^ { \circ } \right)$ 
D) ​ $\frac { 1 } { 2 } \left( \cos 110 ^ { \circ } - i \sin 110 ^ { \circ } \right)$ 
E) ​ $\frac { 1 } { 2 } \left( \cos 50 ^ { \circ } + i \sin 50 ^ { \circ } \right)$

Question 14

Use a graphing utility to represent the complex number in standard form.Round your answer to 4 decimal places.​ $$14 \left( \cos \frac { 2 \pi } { 5 } + i \sin \frac { 2 \pi } { 5 } \right)$$ ​

Accepted Answer

A) 4.3262 + 13.3148i 
B) 13.3148 + 4.3262i 
C) 13.3148 - 4.3262i 
D) 4.3262 - 13.3148i 
E) None of the above 
A) 4.3262 + 13.3148i 
B) 13.3148 + 4.3262i 
C) 13.3148 - 4.3262i 
D) 4.3262 - 13.3148i 
E) None of the above

Question 15

Find the trigonometric form of the complex number represented graphically.

Accepted Answer

A) 3 $\sqrt { 2 }$ (cos(3π/4)+ isin(3π/4)) 
B) -3(cos(7π/4)+ isin(7π/4)) 
C) 3 $\sqrt { 2 }$ (cos(7π/4)+ isin(7π/4)) 
D) -3 $\sqrt { 2 }$ (cos(3π/4)+ isin(3π/4)) 
E) ​3 $\sqrt { 2 }$ (cos(5π/4)+ isin(5π/4)) 
A) 3 $\sqrt { 2 }$ (cos(3π/4)+ isin(3π/4)) 
B) -3(cos(7π/4)+ isin(7π/4)) 
C) 3 $\sqrt { 2 }$ (cos(7π/4)+ isin(7π/4)) 
D) -3 $\sqrt { 2 }$ (cos(3π/4)+ isin(3π/4)) 
E) ​3 $\sqrt { 2 }$ (cos(5π/4)+ isin(5π/4))

Question 16

Use a graphing utility to represent the complex number in standard form.Round your answer to 4 decimal places.​ $$5 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$$ ​

Accepted Answer

A) 4.3301 + 2.5i 
B) 2.5 + 4.3301i 
C) 2.5 - 4.3301i 
D) 4.3301 - 2.5i 
E) None of the above 
A) 4.3301 + 2.5i 
B) 2.5 + 4.3301i 
C) 2.5 - 4.3301i 
D) 4.3301 - 2.5i 
E) None of the above

Question 17

Use a graphing utility to represent the complex number in standard form.Round your answer to 4 decimal places.​ $$2 \left( \cos 154 ^ { \circ } + i \sin 154 ^ { \circ } \right)$$ ​

Accepted Answer

A) 0.8767-1.7976i 
B) -1.7976​ - 0.8767i 
C) ​-1.7976 + 0.8767i 
D) ​-0.8767-1.7976i 
E) None of the above 
A) 0.8767-1.7976i 
B) -1.7976​ - 0.8767i 
C) ​-1.7976 + 0.8767i 
D) ​-0.8767-1.7976i 
E) None of the above

Question 18

Find the trigonometric form of the complex number shown below. -4 + 4 $\sqrt { 3 }$ i

Accepted Answer

A) 4 $\left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$ 
B) 2 $\left( \cos \frac { 4 \pi } { 3 } + i \sin \frac { 4 \pi } { 3 } \right)$ 
C) 8 $\left( \cos \frac { 2 \pi } { 6 } + i \sin \frac { 2 \pi } { 6 } \right)$ 
D) 4 $\left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$ 
E) 8 $\left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$ 
A) 4 $\left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$ 
B) 2 $\left( \cos \frac { 4 \pi } { 3 } + i \sin \frac { 4 \pi } { 3 } \right)$ 
C) 8 $\left( \cos \frac { 2 \pi } { 6 } + i \sin \frac { 2 \pi } { 6 } \right)$ 
D) 4 $\left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$ 
E) 8 $\left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$

Question 19

Find the standard form of the complex number shown below. $$5 \left( \cos \frac { 11 \pi } { 6 } + i \sin \frac { 11 \pi } { 6 } \right)$$

Accepted Answer

A)  $- \frac { 5 \sqrt { 3 } } { 2 } - \frac { 5 } { 2 }$ 
B)  $\frac { 5 \sqrt { 3 } } { 4 } - \frac { 5 } { 4 }$ 
C)  $\frac { 2 } { 5 } - \frac { 2 \sqrt { 3 } } { 5 }$ 
D)  $\frac { 5 \sqrt { 3 } } { 2 } - \frac { 5 } { 2 }$ 
E)  $\frac { 5 \sqrt { 3 } } { 4 } + \frac { 5 } { 4 }$ 
A)  $- \frac { 5 \sqrt { 3 } } { 2 } - \frac { 5 } { 2 }$ 
B)  $\frac { 5 \sqrt { 3 } } { 4 } - \frac { 5 } { 4 }$ 
C)  $\frac { 2 } { 5 } - \frac { 2 \sqrt { 3 } } { 5 }$ 
D)  $\frac { 5 \sqrt { 3 } } { 2 } - \frac { 5 } { 2 }$ 
E)  $\frac { 5 \sqrt { 3 } } { 4 } + \frac { 5 } { 4 }$

Question 20

Perform the operation and leave the result in trigonometric form.​ $$\frac { 2 \left( \cos 70 ^ { \circ } + i \sin 70 ^ { \circ } \right) } { 4 \left( \cos 40 ^ { \circ } + i \sin 40 ^ { \circ } \right) }$$ ​

Accepted Answer

A) ​ $\frac { 1 } { 2 } \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right)$ 
B) ​ $\frac { 1 } { 2 } \left( \cos 40 ^ { \circ } + i \sin 40 ^ { \circ } \right)$ 
C) ​ $\frac { 1 } { 2 } \left( \cos 30 ^ { \circ } - i \sin 30 ^ { \circ } \right)$ 
D) ​ $\frac { 1 } { 2 } \left( \cos 70 ^ { \circ } - i \sin 70 ^ { \circ } \right)$ 
E) ​ $\frac { 1 } { 2 } \left( \cos 70 ^ { \circ } + i \sin 70 ^ { \circ } \right)$ 
A) ​ $\frac { 1 } { 2 } \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right)$ 
B) ​ $\frac { 1 } { 2 } \left( \cos 40 ^ { \circ } + i \sin 40 ^ { \circ } \right)$ 
C) ​ $\frac { 1 } { 2 } \left( \cos 30 ^ { \circ } - i \sin 30 ^ { \circ } \right)$ 
D) ​ $\frac { 1 } { 2 } \left( \cos 70 ^ { \circ } - i \sin 70 ^ { \circ } \right)$ 
E) ​ $\frac { 1 } { 2 } \left( \cos 70 ^ { \circ } + i \sin 70 ^ { \circ } \right)$

Exam 40: Trigonometric Form of a Complex Number

Find all solutions to the following equation. x3+729=0x ^ { 3 } + 729 = 0x3+729=0 ​

Perform the indicated operation using trigonometric form.Leave answer in trigonometric form. (−6−6i)(−5−5i)( - 6 - 6 i ) ( - 5 - 5 i )(−6−6i)(−5−5i)

Find the absolute value of the complex number -3 + 5i.

Find the product (6+6i)(2−2i)( 6 + 6 i ) ( 2 - 2 i )(6+6i)(2−2i) using trigonometric forms.Leave the result in trigonometric form.

Perform the operation and leave the result in trigonometric form.​ (cos⁡7∘+isin⁡7∘)(cos⁡24∘+isin⁡24∘)\left( \cos 7 ^ { \circ } + i \sin 7 ^ { \circ } \right) \left( \cos 24 ^ { \circ } + i \sin 24 ^ { \circ } \right)(cos7∘+isin7∘)(cos24∘+isin24∘) ​

Perform the indicated operation using the standard form.​ 5i(1−2i)5 i ( 1 - \sqrt { 2 } i )5i(1−2​i) ​

Represent the complex number below graphically. 2(cos⁡135∘+isin⁡135∘)2 \left( \cos 135 ^ { \circ } + i \sin 135 ^ { \circ } \right)2(cos135∘+isin135∘)

​Find the absolute value of the complex number 5 + 3i. ​

Find the standard form of the complex number shown below.Round answers to two decimal places. 8(cos⁡245∘+isin⁡245∘)8 \left( \cos 245 ^ { \circ } + i \sin 245 ^ { \circ } \right)8(cos245∘+isin245∘)

Use a graphing utility to represent the complex number in standard form.Round your answer to 4 decimal places.​ 14(cos⁡2π5+isin⁡2π5)14 \left( \cos \frac { 2 \pi } { 5 } + i \sin \frac { 2 \pi } { 5 } \right)14(cos52π​+isin52π​) ​

Find the trigonometric form of the complex number represented graphically.

Use a graphing utility to represent the complex number in standard form.Round your answer to 4 decimal places.​ 5(cos⁡π3+isin⁡π3)5 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)5(cos3π​+isin3π​) ​

Use a graphing utility to represent the complex number in standard form.Round your answer to 4 decimal places.​ 2(cos⁡154∘+isin⁡154∘)2 \left( \cos 154 ^ { \circ } + i \sin 154 ^ { \circ } \right)2(cos154∘+isin154∘) ​

Find the trigonometric form of the complex number shown below. -4 + 4 3\sqrt { 3 }3​ i

Find the standard form of the complex number shown below. 5(cos⁡11π6+isin⁡11π6)5 \left( \cos \frac { 11 \pi } { 6 } + i \sin \frac { 11 \pi } { 6 } \right)5(cos611π​+isin611π​)

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Ellipses

Hyperbolas

Rotation of Conics

Parametric Equations

Polar Coordinates

Find all solutions to the following equation. $x ^ { 3 } + 729 = 0$

Perform the indicated operation using trigonometric form.Leave answer in trigonometric form. $( - 6 - 6 i ) ( - 5 - 5 i )$

Find the product $( 6 + 6 i ) ( 2 - 2 i )$ using trigonometric forms.Leave the result in trigonometric form.

Perform the operation and leave the result in trigonometric form. $\left( \cos 7 ^ { \circ } + i \sin 7 ^ { \circ } \right) \left( \cos 24 ^ { \circ } + i \sin 24 ^ { \circ } \right)$

Perform the indicated operation using the standard form. $5 i ( 1 - \sqrt { 2 } i )$

Represent the complex number below graphically. $2 \left( \cos 135 ^ { \circ } + i \sin 135 ^ { \circ } \right)$ $Represent the complex number below graphically. 2 \left( \cos 135 ^ { \circ } + i \sin 135 ^ { \circ } \right)$

Find the absolute value of the complex number 5 + 3i.

Find the standard form of the complex number shown below.Round answers to two decimal places. $8 \left( \cos 245 ^ { \circ } + i \sin 245 ^ { \circ } \right)$

Use a graphing utility to represent the complex number in standard form.Round your answer to 4 decimal places. $14 \left( \cos \frac { 2 \pi } { 5 } + i \sin \frac { 2 \pi } { 5 } \right)$

Use a graphing utility to represent the complex number in standard form.Round your answer to 4 decimal places. $5 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$

Use a graphing utility to represent the complex number in standard form.Round your answer to 4 decimal places. $2 \left( \cos 154 ^ { \circ } + i \sin 154 ^ { \circ } \right)$

Find the trigonometric form of the complex number shown below. -4 + 4 $\sqrt { 3 }$ i

Find the standard form of the complex number shown below. $5 \left( \cos \frac { 11 \pi } { 6 } + i \sin \frac { 11 \pi } { 6 } \right)$