Question 1

Perform the indicated operation using trigonometric form.Leave the answer in trigonometric forms. $$( 2 + 2 i ) ( - 1 - i )$$ ​

Accepted Answer

A)  $- 2 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$ 
B) ​ $4 \left( \cos \frac { 3 \pi } { 2 } - i \sin \frac { 3 \pi } { 2 } \right)$ 
C) ​ $4 \left( \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right)$ 
D) ​ $- 2 \left( \cos \frac { 3 \pi } { 4 } + i \sin \frac { 3 \pi } { 4 } \right)$ 
E) ​ $2 \left( \cos \frac { 5 \pi } { 4 } + i \sin \frac { 5 \pi } { 4 } \right)$ 
A)  $- 2 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$ 
B) ​ $4 \left( \cos \frac { 3 \pi } { 2 } - i \sin \frac { 3 \pi } { 2 } \right)$ 
C) ​ $4 \left( \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right)$ 
D) ​ $- 2 \left( \cos \frac { 3 \pi } { 4 } + i \sin \frac { 3 \pi } { 4 } \right)$ 
E) ​ $2 \left( \cos \frac { 5 \pi } { 4 } + i \sin \frac { 5 \pi } { 4 } \right)$

Question 2

Plot the following complex number. -3

Accepted Answer

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

Question 3

Perform the operation shown below and leave the result in trigonometric form. $$\frac { 48 ( \cos 2.5 + i \sin 2.5 ) } { 8 ( \cos 1.3 + i \sin 1.3 ) }$$

Accepted Answer

A)  $6 ( \cos 1.2 + i \sin 1.2 )$ 
B)  $6 ( \cos 2.5 + i \sin 2.5 )$ 
C)  $6 ( \cos 1.3 + i \sin 1.3 )$ 
D)  $8 ( \cos 1.2 + i \sin 1.2 )$ 
E)  $48 ( \cos 1.2 + i \sin 1.2 )$ 
A)  $6 ( \cos 1.2 + i \sin 1.2 )$ 
B)  $6 ( \cos 2.5 + i \sin 2.5 )$ 
C)  $6 ( \cos 1.3 + i \sin 1.3 )$ 
D)  $8 ( \cos 1.2 + i \sin 1.2 )$ 
E)  $48 ( \cos 1.2 + i \sin 1.2 )$

Question 4

Perform the operation and leave the result in trigonometric form.​ $$\frac { 5 \left( \cos 4.5 ^ { \circ } + i \sin 4.5 ^ { \circ } \right) } { 4 \left( \cos 2.4 ^ { \circ } + i \sin 2.4 ^ { \circ } \right) }$$ ​

Accepted Answer

A)  $\frac { 5 } { 4 } \left( \cos 4.5 ^ { \circ } + i \sin 4.5 ^ { \circ } \right)$ 
B) ​ $\frac { 5 } { 4 } \left( \cos 2.1 ^ { \circ } - i \sin 2.1 ^ { \circ } \right)$ 
C) ​ $\frac { 5 } { 4 } \left( \cos 2.1 ^ { \circ } + i \sin 2.1 ^ { \circ } \right)$ 
D) ​ $\frac { 5 } { 4 } \left( \cos 4.5 ^ { \circ } - i \sin 4.5 ^ { \circ } \right)$ 
E) ​ $\frac { 5 } { 4 } \left( \cos 2.4 ^ { \circ } + i \sin 2.4 ^ { \circ } \right)$ 
A)  $\frac { 5 } { 4 } \left( \cos 4.5 ^ { \circ } + i \sin 4.5 ^ { \circ } \right)$ 
B) ​ $\frac { 5 } { 4 } \left( \cos 2.1 ^ { \circ } - i \sin 2.1 ^ { \circ } \right)$ 
C) ​ $\frac { 5 } { 4 } \left( \cos 2.1 ^ { \circ } + i \sin 2.1 ^ { \circ } \right)$ 
D) ​ $\frac { 5 } { 4 } \left( \cos 4.5 ^ { \circ } - i \sin 4.5 ^ { \circ } \right)$ 
E) ​ $\frac { 5 } { 4 } \left( \cos 2.4 ^ { \circ } + i \sin 2.4 ^ { \circ } \right)$

Question 5

Use DeMoivre's Theorem to find the indicated power of the following complex number. $\left[ - 2 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right) \right] ^ { 6 }$

Accepted Answer

A) -4 
B) -8 
C)  $64 + 64 \sqrt { 3 }$ 
D)  $32 + 32 \sqrt { 3 }$ 
E) 8 
A) -4 
B) -8 
C)  $64 + 64 \sqrt { 3 }$ 
D)  $32 + 32 \sqrt { 3 }$ 
E) 8

Question 6

Find the trigonometric form of the complex number shown below. 10i

Accepted Answer

A) ​ $10 ( \cos \pi + i \sin \pi )$ 
B) ​ $10 \left( \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right)$ 
C) ​ $10 ( \cos 0 + i \sin 0 )$ 
D) ​ $10 \left( \cos \frac { \pi } { 4 } + i \sin \frac { \pi } { 4 } \right)$ 
E)  $10 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$ 
A) ​ $10 ( \cos \pi + i \sin \pi )$ 
B) ​ $10 \left( \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right)$ 
C) ​ $10 ( \cos 0 + i \sin 0 )$ 
D) ​ $10 \left( \cos \frac { \pi } { 4 } + i \sin \frac { \pi } { 4 } \right)$ 
E)  $10 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$

Question 7

Perform the operation shown below and leave the result in trigonometric form. $$\left[ 3 \left( \cos 100 ^ { \circ } + i \sin 100 ^ { \circ } \right) \right] \left[ 6 \left( \cos 230 ^ { \circ } + i \sin 230 ^ { \circ } \right) \right]$$

Accepted Answer

A)  $18 \left( \cos 230 ^ { \circ } + i \sin 230 ^ { \circ } \right)$ 
B) ​ $18 \left( \cos 130 ^ { \circ } + i \sin 130 ^ { \circ } \right)$ 
C) ​ $18 \left( \cos 330 ^ { \circ } + i \sin 330 ^ { \circ } \right)$ 
D) ​ $9 \left( \cos 330 ^ { \circ } + \sin 330 ^ { \circ } \right)$ 
E) ​ $9 \left( \cos 130 ^ { \circ } + i \sin 130 ^ { \circ } \right)$ 
A)  $18 \left( \cos 230 ^ { \circ } + i \sin 230 ^ { \circ } \right)$ 
B) ​ $18 \left( \cos 130 ^ { \circ } + i \sin 130 ^ { \circ } \right)$ 
C) ​ $18 \left( \cos 330 ^ { \circ } + i \sin 330 ^ { \circ } \right)$ 
D) ​ $9 \left( \cos 330 ^ { \circ } + \sin 330 ^ { \circ } \right)$ 
E) ​ $9 \left( \cos 130 ^ { \circ } + i \sin 130 ^ { \circ } \right)$

Question 8

Find the fourth roots of $- \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } i$ Write the roots in trigonometric form.

Accepted Answer

A)  $$\begin{array} { l } 
w _ { 1 } = \cos \left( 20 ^ { \circ } \right) + i \sin \left( 20 ^ { \circ } \right) \
w _ { 2 } = \cos \left( 110 ^ { \circ } \right) + i \sin \left( 110 ^ { \circ } \right) \
w _ { 3 } = \cos \left( 200 ^ { \circ } \right) + i \sin \left( 200 ^ { \circ } \right) \
w _ { 4 } = \cos \left( 290 ^ { \circ } \right) + i \sin \left( 290 ^ { \circ } \right)
\end{array}$$ 
B)  $$\begin{array} { l } 
w _ { 1 } = \cos \left( 30 ^ { \circ } \right) + i \sin \left( 30 ^ { \circ } \right) \
w _ { 2 } = \cos \left( 120 ^ { \circ } \right) + i \sin \left( 120 ^ { \circ } \right) \
w _ { 3 } = \cos \left( 210 ^ { \circ } \right) + i \sin \left( 210 ^ { \circ } \right) \
w _ { 4 } = \cos \left( 300 ^ { \circ } \right) + i \sin \left( 300 ^ { \circ } \right)
\end{array}$$ 
C)  $$\begin{array} { l } 
w _ { 1 } = \cos \left( 35 ^ { \circ } \right) + i \sin \left( 35 ^ { \circ } \right) \
w _ { 2 } = \cos \left( 125 ^ { \circ } \right) + i \sin \left( 125 ^ { \circ } \right) \
w _ { 3 } = \cos \left( 215 ^ { \circ } \right) + i \sin \left( 215 ^ { \circ } \right) \
w _ { 4 } = \cos \left( 305 ^ { \circ } \right) + i \sin \left( 305 ^ { \circ } \right)
\end{array}$$ 
D)  $$\begin{array} { l } 
w _ { 1 } = \cos \left( 25 ^ { \circ } \right) + i \sin \left( 25 ^ { \circ } \right) \
w _ { 2 } = \cos \left( 115 ^ { \circ } \right) + i \sin \left( 115 ^ { \circ } \right) \
w _ { 3 } = \cos \left( 205 ^ { \circ } \right) + i \sin \left( 205 ^ { \circ } \right) \
w _ { 4 } = \cos \left( 295 ^ { \circ } \right) + i \sin \left( 295 ^ { \circ } \right)
\end{array}$$ 
E)  $$\begin{array} { l } 
w _ { 1 } = \cos \left( 40 ^ { \circ } \right) + i \sin \left( 40 ^ { \circ } \right) \
w _ { 2 } = \cos \left( 130 ^ { \circ } \right) + i \sin \left( 130 ^ { \circ } \right) \
w _ { 3 } = \cos \left( 220 ^ { \circ } \right) + i \sin \left( 220 ^ { \circ } \right) \
w _ { 4 } = \cos \left( 310 ^ { \circ } \right) + i \sin \left( 310 ^ { \circ } \right)
\end{array}$$ 
A)  $$\begin{array} { l } 
w _ { 1 } = \cos \left( 20 ^ { \circ } \right) + i \sin \left( 20 ^ { \circ } \right) \
w _ { 2 } = \cos \left( 110 ^ { \circ } \right) + i \sin \left( 110 ^ { \circ } \right) \
w _ { 3 } = \cos \left( 200 ^ { \circ } \right) + i \sin \left( 200 ^ { \circ } \right) \
w _ { 4 } = \cos \left( 290 ^ { \circ } \right) + i \sin \left( 290 ^ { \circ } \right)
\end{array}$$ 
B)  $$\begin{array} { l } 
w _ { 1 } = \cos \left( 30 ^ { \circ } \right) + i \sin \left( 30 ^ { \circ } \right) \
w _ { 2 } = \cos \left( 120 ^ { \circ } \right) + i \sin \left( 120 ^ { \circ } \right) \
w _ { 3 } = \cos \left( 210 ^ { \circ } \right) + i \sin \left( 210 ^ { \circ } \right) \
w _ { 4 } = \cos \left( 300 ^ { \circ } \right) + i \sin \left( 300 ^ { \circ } \right)
\end{array}$$ 
C)  $$\begin{array} { l } 
w _ { 1 } = \cos \left( 35 ^ { \circ } \right) + i \sin \left( 35 ^ { \circ } \right) \
w _ { 2 } = \cos \left( 125 ^ { \circ } \right) + i \sin \left( 125 ^ { \circ } \right) \
w _ { 3 } = \cos \left( 215 ^ { \circ } \right) + i \sin \left( 215 ^ { \circ } \right) \
w _ { 4 } = \cos \left( 305 ^ { \circ } \right) + i \sin \left( 305 ^ { \circ } \right)
\end{array}$$ 
D)  $$\begin{array} { l } 
w _ { 1 } = \cos \left( 25 ^ { \circ } \right) + i \sin \left( 25 ^ { \circ } \right) \
w _ { 2 } = \cos \left( 115 ^ { \circ } \right) + i \sin \left( 115 ^ { \circ } \right) \
w _ { 3 } = \cos \left( 205 ^ { \circ } \right) + i \sin \left( 205 ^ { \circ } \right) \
w _ { 4 } = \cos \left( 295 ^ { \circ } \right) + i \sin \left( 295 ^ { \circ } \right)
\end{array}$$ 
E)  $$\begin{array} { l } 
w _ { 1 } = \cos \left( 40 ^ { \circ } \right) + i \sin \left( 40 ^ { \circ } \right) \
w _ { 2 } = \cos \left( 130 ^ { \circ } \right) + i \sin \left( 130 ^ { \circ } \right) \
w _ { 3 } = \cos \left( 220 ^ { \circ } \right) + i \sin \left( 220 ^ { \circ } \right) \
w _ { 4 } = \cos \left( 310 ^ { \circ } \right) + i \sin \left( 310 ^ { \circ } \right)
\end{array}$$

Question 9

Perform the operation shown below and leave the result in trigonometric form. ​​ $$\frac { 12 ( \cos 3.1 + i \sin 3.1 ) } { 6 ( \cos 2.7 + i \sin 2.7 ) }$$

Accepted Answer

A)  $6 ( \cos 0.4 + i \sin 0.4 )$ 
B) ​ $6 ( \cos 1.1 + i \sin 1.1 )$ 
C) ​ $2 ( \cos 0.4 + i \sin 0.4 )$ 
D) ​ $2 ( \cos 8.37 + i \sin 8.37 )$ 
E) ​ $2 ( \cos 5.8 + i \sin 5.8 )$ 
A)  $6 ( \cos 0.4 + i \sin 0.4 )$ 
B) ​ $6 ( \cos 1.1 + i \sin 1.1 )$ 
C) ​ $2 ( \cos 0.4 + i \sin 0.4 )$ 
D) ​ $2 ( \cos 8.37 + i \sin 8.37 )$ 
E) ​ $2 ( \cos 5.8 + i \sin 5.8 )$

Question 10

Plot the complex number and find its absolute value. ​
-5 + 10i
​

Accepted Answer

A) ​   ​
|-5 + 10i| = $\sqrt { 95 }$ 
B) ​   ​
|-5 + 10i| = $2 \sqrt { 7 }$ 
C) ​   ​
|-5 + 10i| = $5 \sqrt { 5 }$ 
D) ​   ​
|-5 + 10i| = $\sqrt { 22 }$ 
E) ​   ​
|-5 + 10i| = $\sqrt { 105 }$ 
A) ​   ​
|-5 + 10i| = $\sqrt { 95 }$ 
B) ​   ​
|-5 + 10i| = $2 \sqrt { 7 }$ 
C) ​   ​
|-5 + 10i| = $5 \sqrt { 5 }$ 
D) ​   ​
|-5 + 10i| = $\sqrt { 22 }$ 
E) ​   ​
|-5 + 10i| = $\sqrt { 105 }$

Question 11

Divide the complex numbers below and leave the result in trigonometric form. $$\frac { 4 ( \cos ( 7 \pi / 10 ) + i \sin ( 7 \pi / 10 ) ) } { 10 ( \cos ( 3 \pi / 7 ) + i \sin ( 3 \pi / 7 ) ) }$$

Accepted Answer

A)  $\cos \frac { 79 } { 70 } \pi + i \sin \frac { 79 } { 70 } \pi$ ​ 
B) ​ $\cos \frac { 19 } { 70 } \pi + i \sin \frac { 19 } { 70 } \pi$ 
C) ​ $\frac { 2 } { 5 } \left( \cos \frac { 79 } { 70 } \pi + i \sin \frac { 79 } { 70 } \pi \right)$ 
D) ​ $\frac { 2 } { 5 } \left( \cos \frac { 2 } { 35 } \pi + i \sin \frac { 2 } { 35 } \pi \right)$ 
E) ​ $\frac { 2 } { 5 } \left( \cos \frac { 19 } { 70 } \pi + i \sin \frac { 19 } { 70 } \pi \right)$ 
A)  $\cos \frac { 79 } { 70 } \pi + i \sin \frac { 79 } { 70 } \pi$ ​ 
B) ​ $\cos \frac { 19 } { 70 } \pi + i \sin \frac { 19 } { 70 } \pi$ 
C) ​ $\frac { 2 } { 5 } \left( \cos \frac { 79 } { 70 } \pi + i \sin \frac { 79 } { 70 } \pi \right)$ 
D) ​ $\frac { 2 } { 5 } \left( \cos \frac { 2 } { 35 } \pi + i \sin \frac { 2 } { 35 } \pi \right)$ 
E) ​ $\frac { 2 } { 5 } \left( \cos \frac { 19 } { 70 } \pi + i \sin \frac { 19 } { 70 } \pi \right)$

Question 12

Find the cube roots of the following complex number.Write each of the roots in standard form. -1

Accepted Answer

A)  $- 5 , - \frac { 5 } { 2 } - \frac { 5 \sqrt { 3 } } { 2 } i , - \frac { 5 } { 2 } + \frac { 5 \sqrt { 3 } } { 2 } i$ 
B)  $- 5,5$ 
C) -1 
D)  $- 5 , \frac { 5 } { 2 } - \frac { 5 \sqrt { 3 } } { 2 } i , \frac { 5 } { 2 } + \frac { 5 \sqrt { 3 } } { 2 } i$ 
E)  $5 , - \frac { 5 } { 2 } + \frac { 5 \sqrt { 3 } } { 2 } i , - \frac { 5 } { 2 } - \frac { 5 \sqrt { 3 } } { 2 } i$ 
A)  $- 5 , - \frac { 5 } { 2 } - \frac { 5 \sqrt { 3 } } { 2 } i , - \frac { 5 } { 2 } + \frac { 5 \sqrt { 3 } } { 2 } i$ 
B)  $- 5,5$ 
C) -1 
D)  $- 5 , \frac { 5 } { 2 } - \frac { 5 \sqrt { 3 } } { 2 } i , \frac { 5 } { 2 } + \frac { 5 \sqrt { 3 } } { 2 } i$ 
E)  $5 , - \frac { 5 } { 2 } + \frac { 5 \sqrt { 3 } } { 2 } i , - \frac { 5 } { 2 } - \frac { 5 \sqrt { 3 } } { 2 } i$

Question 13

Select the graph of all complex numbers z satisfying the given condition.​ $| z | = 4$ ​

Accepted Answer

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

Question 14

Find the standard form of the complex number $$5 \left( \cos \left( 25 ^ { \circ } 46 ^ { \prime } \right) + i \sin \left( 25 ^ { \circ } 46 ^ { \prime } \right) \right)$$ .Round values to the nearest hundredth.

Accepted Answer

A)  $4.91 + 1.36 i$ 
B)  $4.5 + 2.17 i$ 
C)  $- 4.5 - 2.17 i$ 
D)  $- 2.81 - 2.92 i$ 
E)  $2.81 + 2.92 i$ 
A)  $4.91 + 1.36 i$ 
B)  $4.5 + 2.17 i$ 
C)  $- 4.5 - 2.17 i$ 
D)  $- 2.81 - 2.92 i$ 
E)  $2.81 + 2.92 i$

Question 15

Find the standard form of the complex number $8 \left( \cos 330 ^ { \circ } \right) + i \sin 330 ^ { \circ }$ . ​

Accepted Answer

A) ​8 $$\sqrt { 3 }$$ - 8i 
B) ​-4 $\sqrt { 3 }$ + 4i 
C) ​4 $$\sqrt { 3 }$$ - 4i 
D) ​-8 $\sqrt { 3 }$ + 8i 
E) ​4 + 4 $\sqrt { 3 }$ i 
A) ​8 $$\sqrt { 3 }$$ - 8i 
B) ​-4 $\sqrt { 3 }$ + 4i 
C) ​4 $$\sqrt { 3 }$$ - 4i 
D) ​-8 $\sqrt { 3 }$ + 8i 
E) ​4 + 4 $\sqrt { 3 }$ i

Question 16

Find the standard form of the complex number shown below.Round answers to two decimal places.​ $$2 \left( \cos 230 ^ { \circ } + i \sin 230 ^ { \circ } \right)$$

Accepted Answer

A) ​-1.29 - 1.53i 
B) ​-2.53 - 2.88i 
C) ​-2.04 - 2.63i 
D) ​-1.52 - 1.92i 
E) ​-2.71 - 3.06i 
A) ​-1.29 - 1.53i 
B) ​-2.53 - 2.88i 
C) ​-2.04 - 2.63i 
D) ​-1.52 - 1.92i 
E) ​-2.71 - 3.06i

Question 17

Divide the complex numbers below and leave the result in trigonometric form. $$\frac { 2 \left( \cos 190 ^ { \circ } + i \sin 190 ^ { \circ } \right) } { 9 \left( \cos 190 ^ { \circ } + i \sin 190 ^ { \circ } \right) }$$

Accepted Answer

A)  $\frac { 2 } { 9 } \left( \cos 360 ^ { \circ } + i \sin 360 ^ { \circ } \right)$ 
B)  $\frac { 2 } { 9 } \left( \cos 20 ^ { \circ } + i \sin 20 ^ { \circ } \right)$ 
C)  $\frac { 2 } { 9 } \left( \cos 360 ^ { \circ } + i \sin 20 ^ { \circ } \right)$ 
D)  $18 \left( \cos 360 ^ { \circ } + i \sin 360 ^ { \circ } \right)$ 
E)  $18 \left( \cos 20 ^ { \circ } + i \sin 20 ^ { \circ } \right)$ 
A)  $\frac { 2 } { 9 } \left( \cos 360 ^ { \circ } + i \sin 360 ^ { \circ } \right)$ 
B)  $\frac { 2 } { 9 } \left( \cos 20 ^ { \circ } + i \sin 20 ^ { \circ } \right)$ 
C)  $\frac { 2 } { 9 } \left( \cos 360 ^ { \circ } + i \sin 20 ^ { \circ } \right)$ 
D)  $18 \left( \cos 360 ^ { \circ } + i \sin 360 ^ { \circ } \right)$ 
E)  $18 \left( \cos 20 ^ { \circ } + i \sin 20 ^ { \circ } \right)$

Question 18

Find the standard form of the complex number.Then represent the complex number graphically.​ $$6 ( \cos 0 + i \sin 0 )$$ ​

Accepted Answer

A) ​   ​6 
B) ​   6 
C) ​   ​-6​ 
D) ​   -6​ 
E)    6​ 
A) ​   ​6 
B) ​   6 
C) ​   ​-6​ 
D) ​   -6​ 
E)    6​

Question 19

Represent the complex number graphically,and find the trigonometric form of the number. ​
5 - 5i
​

Accepted Answer

A) ​   $$5 \sqrt { 2 } \left( \cos \frac { 7 \pi } { 4 } + i \sin \frac { 7 \pi } { 4 } \right)$$ 
B) ​   $$5 \sqrt { 2 } \left( \cos \frac { 7 \pi } { 4 } + i \sin \frac { 7 \pi } { 4 } \right)$$ 
C) ​   $$\sqrt { 50 } \left( \cos \frac { \pi } { 4 } + \sin \frac { \pi } { 4 } \right)$$ 
D) ​   $$\sqrt { 50 } \left( \cos \frac { \pi } { 4 } - i \sin \frac { \pi } { 4 } \right)$$ 
E) ​   $$\sqrt { 2 } \left( \cos \frac { \pi } { 4 } + i \sin \frac { \pi } { 4 } \right)$$ 
A) ​   $$5 \sqrt { 2 } \left( \cos \frac { 7 \pi } { 4 } + i \sin \frac { 7 \pi } { 4 } \right)$$ 
B) ​   $$5 \sqrt { 2 } \left( \cos \frac { 7 \pi } { 4 } + i \sin \frac { 7 \pi } { 4 } \right)$$ 
C) ​   $$\sqrt { 50 } \left( \cos \frac { \pi } { 4 } + \sin \frac { \pi } { 4 } \right)$$ 
D) ​   $$\sqrt { 50 } \left( \cos \frac { \pi } { 4 } - i \sin \frac { \pi } { 4 } \right)$$ 
E) ​   $$\sqrt { 2 } \left( \cos \frac { \pi } { 4 } + i \sin \frac { \pi } { 4 } \right)$$

Question 20

Plot the complex number 2.   ​

Accepted Answer

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

Exam 40: Trigonometric Form of a Complex Number

Perform the indicated operation using trigonometric form.Leave the answer in trigonometric forms. (2+2i)(−1−i)( 2 + 2 i ) ( - 1 - i )(2+2i)(−1−i) ​

Plot the following complex number. -3

Perform the operation shown below and leave the result in trigonometric form. 48(cos⁡2.5+isin⁡2.5)8(cos⁡1.3+isin⁡1.3)\frac { 48 ( \cos 2.5 + i \sin 2.5 ) } { 8 ( \cos 1.3 + i \sin 1.3 ) }8(cos1.3+isin1.3)48(cos2.5+isin2.5)​

Use DeMoivre's Theorem to find the indicated power of the following complex number. [−2(cos⁡π3+isin⁡π3)]6\left[ - 2 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right) \right] ^ { 6 }[−2(cos3π​+isin3π​)]6

Find the trigonometric form of the complex number shown below. 10i

Find the fourth roots of −12+32i- \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } i−21​+23​​i Write the roots in trigonometric form.

Perform the operation shown below and leave the result in trigonometric form. ​​ 12(cos⁡3.1+isin⁡3.1)6(cos⁡2.7+isin⁡2.7)\frac { 12 ( \cos 3.1 + i \sin 3.1 ) } { 6 ( \cos 2.7 + i \sin 2.7 ) }6(cos2.7+isin2.7)12(cos3.1+isin3.1)​

Plot the complex number and find its absolute value. ​ -5 + 10i ​

Find the cube roots of the following complex number.Write each of the roots in standard form. -1

Select the graph of all complex numbers z satisfying the given condition.​ ∣z∣=4| z | = 4∣z∣=4 ​

Find the standard form of the complex number 5(cos⁡(25∘46′)+isin⁡(25∘46′))5 \left( \cos \left( 25 ^ { \circ } 46 ^ { \prime } \right) + i \sin \left( 25 ^ { \circ } 46 ^ { \prime } \right) \right)5(cos(25∘46′)+isin(25∘46′)) .Round values to the nearest hundredth.

Find the standard form of the complex number 8(cos⁡330∘)+isin⁡330∘8 \left( \cos 330 ^ { \circ } \right) + i \sin 330 ^ { \circ }8(cos330∘)+isin330∘ . ​

Find the standard form of the complex number shown below.Round answers to two decimal places.​ 2(cos⁡230∘+isin⁡230∘)2 \left( \cos 230 ^ { \circ } + i \sin 230 ^ { \circ } \right)2(cos230∘+isin230∘)

Find the standard form of the complex number.Then represent the complex number graphically.​ 6(cos⁡0+isin⁡0)6 ( \cos 0 + i \sin 0 )6(cos0+isin0) ​

Represent the complex number graphically,and find the trigonometric form of the number. ​ 5 - 5i ​

Plot the complex number 2. ​

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

Perform the indicated operation using trigonometric form.Leave the answer in trigonometric forms. $( 2 + 2 i ) ( - 1 - i )$

Perform the operation shown below and leave the result in trigonometric form. $\frac { 48 ( \cos 2.5 + i \sin 2.5 ) } { 8 ( \cos 1.3 + i \sin 1.3 ) }$

Use DeMoivre's Theorem to find the indicated power of the following complex number. $\left[ - 2 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right) \right] ^ { 6 }$

Find the fourth roots of $- \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } i$ Write the roots in trigonometric form.

Perform the operation shown below and leave the result in trigonometric form. $\frac { 12 ( \cos 3.1 + i \sin 3.1 ) } { 6 ( \cos 2.7 + i \sin 2.7 ) }$

Plot the complex number and find its absolute value. -5 + 10i

Select the graph of all complex numbers z satisfying the given condition. $| z | = 4$

Find the standard form of the complex number $5 \left( \cos \left( 25 ^ { \circ } 46 ^ { \prime } \right) + i \sin \left( 25 ^ { \circ } 46 ^ { \prime } \right) \right)$ .Round values to the nearest hundredth.

Find the standard form of the complex number $8 \left( \cos 330 ^ { \circ } \right) + i \sin 330 ^ { \circ }$ .

Find the standard form of the complex number shown below.Round answers to two decimal places. $2 \left( \cos 230 ^ { \circ } + i \sin 230 ^ { \circ } \right)$

Find the standard form of the complex number.Then represent the complex number graphically. $6 ( \cos 0 + i \sin 0 )$

Represent the complex number graphically,and find the trigonometric form of the number. 5 - 5i

Plot the complex number 2.