Question 1

Find the trigonometric form of the complex number shown below. $6 i$

Accepted Answer

A)  $6 ( \cos \pi + i \sin \pi )$ 
B)  $6 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$ 
C)  $6 \left( \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right)$ 
D)  $6 \left( \cos \frac { \pi } { 4 } + i \sin \frac { \pi } { 4 } \right)$ 
E)  $6 ( \cos 0 + i \sin 0 )$ 
A)  $6 ( \cos \pi + i \sin \pi )$ 
B)  $6 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$ 
C)  $6 \left( \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right)$ 
D)  $6 \left( \cos \frac { \pi } { 4 } + i \sin \frac { \pi } { 4 } \right)$ 
E)  $6 ( \cos 0 + i \sin 0 )$

Question 2

Find the trigonometric form of the complex number shown below. ​
​-8

Accepted Answer

A) ​ $$8 \left( \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right)$$ 
B) ​ $8 \left( \cos \frac { \pi } { 4 } + i \sin \frac { \pi } { 4 } \right)$ 
C) ​ $8 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$ 
D) ​ $8 ( \cos 0 + i \sin 0 )$ 
E)  $8 ( \cos \pi + i \sin \pi )$ 
A) ​ $$8 \left( \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right)$$ 
B) ​ $8 \left( \cos \frac { \pi } { 4 } + i \sin \frac { \pi } { 4 } \right)$ 
C) ​ $8 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$ 
D) ​ $8 ( \cos 0 + i \sin 0 )$ 
E)  $8 ( \cos \pi + i \sin \pi )$

Question 3

Write the complex number shown below in trigonometric form.

Accepted Answer

A)  $6 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$ 
B)  $6 \left( \cos \frac { 5 \pi } { 3 } + i \sin \frac { 5 \pi } { 3 } \right)$ 
C)  $6 \left( \cos \frac { 11 \pi } { 6 } + i \sin \frac { 11 \pi } { 6 } \right)$ 
D)  $6 \left( \cos \frac { 4 \pi } { 3 } + i \sin \frac { 4 \pi } { 3 } \right)$ 
E)  $6 \left( \cos \frac { 5 \pi } { 4 } + i \sin \frac { 5 \pi } { 4 } \right)$ 
A)  $6 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$ 
B)  $6 \left( \cos \frac { 5 \pi } { 3 } + i \sin \frac { 5 \pi } { 3 } \right)$ 
C)  $6 \left( \cos \frac { 11 \pi } { 6 } + i \sin \frac { 11 \pi } { 6 } \right)$ 
D)  $6 \left( \cos \frac { 4 \pi } { 3 } + i \sin \frac { 4 \pi } { 3 } \right)$ 
E)  $6 \left( \cos \frac { 5 \pi } { 4 } + i \sin \frac { 5 \pi } { 4 } \right)$

Question 4

Find the standard form of the complex number shown below. $$3 \left( \cos \frac { 7 \pi } { 6 } + i \sin \frac { 7 \pi } { 6 } \right)$$

Accepted Answer

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

Question 5

Find the product $$( - 5 + 5 i ) ( 7 - 7 i )$$ using trigonometric forms.Leave the result in trigonometric form.

Accepted Answer

A)  $35 \left( \cos 135 ^ { \circ } + i \sin 135 ^ { \circ } \right)$ 
B) ​ $70 \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right)$ 
C) ​ $35 \left( \cos 90 ^ { \circ } + i \sin 90 ^ { \circ } \right)$ 
D) ​ $70 \left( \cos 135 ^ { \circ } + i \sin 135 ^ { \circ } \right)$ 
E) ​ $70 \left( \cos 90 ^ { \circ } + i \sin 90 ^ { \circ } \right)$ 
A)  $35 \left( \cos 135 ^ { \circ } + i \sin 135 ^ { \circ } \right)$ 
B) ​ $70 \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right)$ 
C) ​ $35 \left( \cos 90 ^ { \circ } + i \sin 90 ^ { \circ } \right)$ 
D) ​ $70 \left( \cos 135 ^ { \circ } + i \sin 135 ^ { \circ } \right)$ 
E) ​ $70 \left( \cos 90 ^ { \circ } + i \sin 90 ^ { \circ } \right)$

Question 6

Plot the complex number and find its absolute value. ​
-5 + 2i
​

Accepted Answer

A) ​   ​ $$| - 5 + 2 i | = \sqrt { - 1 }$$ 
B) ​   ​ $$| - 5 + 2 i | = \sqrt { 28 }$$ 
C) ​   ​ $$| - 5 + 2 i | = \sqrt { 29 }$$ 
D) ​   ​ $$| - 5 + 2 i | = \sqrt { 2 }$$ 
E) ​   ​ $$| - 5 + 2 i | = \sqrt { 9 }$$ 
A) ​   ​ $$| - 5 + 2 i | = \sqrt { - 1 }$$ 
B) ​   ​ $$| - 5 + 2 i | = \sqrt { 28 }$$ 
C) ​   ​ $$| - 5 + 2 i | = \sqrt { 29 }$$ 
D) ​   ​ $$| - 5 + 2 i | = \sqrt { 2 }$$ 
E) ​   ​ $$| - 5 + 2 i | = \sqrt { 9 }$$

Question 7

Perform the indicated operation in trigonometric form.Write the solution in standard form rounded to four decimal places. $$\frac { 4 + i \sqrt { 3 } } { 8 - 3 i }$$ ​

Accepted Answer

A) 0.4682 + 0.2027i 
B) 0.4777 - 0.1791i 
C) 0.7197 + 0.6943i 
D) 0.5095 + 0.0254i 
E) 0.3672 + 0.3542i 
A) 0.4682 + 0.2027i 
B) 0.4777 - 0.1791i 
C) 0.7197 + 0.6943i 
D) 0.5095 + 0.0254i 
E) 0.3672 + 0.3542i

Question 8

Represent the complex number below graphically. $$\sqrt { 3 } + i$$

Accepted Answer

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

Question 9

Plot the complex number and find its absolute value. ​
-5 + 9i
​

Accepted Answer

A) ​   ​
|-5 + 9i| = $2 \sqrt { 19 }$ 
B) ​   ​
|-5 + 9i| = $2 \sqrt { 7 }$ 
C) ​   ​
|-5 + 9i| = $\sqrt { 106 }$ 
D) ​   ​
|-5 + 9i| = $\sqrt { 22 }$ 
E) ​   ​
|-5 + 9i| = $\sqrt { 86 }$ 
A) ​   ​
|-5 + 9i| = $2 \sqrt { 19 }$ 
B) ​   ​
|-5 + 9i| = $2 \sqrt { 7 }$ 
C) ​   ​
|-5 + 9i| = $\sqrt { 106 }$ 
D) ​   ​
|-5 + 9i| = $\sqrt { 22 }$ 
E) ​   ​
|-5 + 9i| = $\sqrt { 86 }$

Question 10

Represent the complex number graphically. ​
2
​

Accepted Answer

A) ​   $$Z = 2 ( \cos 0 - i \sin 0 )$$ 
B) ​   $$Z = 2 ( \cos 0 + i \sin 0 )$$ 
C) ​   $$Z = 2 ( \cos 0 - i \sin 0 )$$ 
D) ​   $$Z = 2 ( \cos 0 + i \sin 0 )$$ 
E) ​   $$Z = 2 ( \cos 0 - i \sin 0 )$$ 
A) ​   $$Z = 2 ( \cos 0 - i \sin 0 )$$ 
B) ​   $$Z = 2 ( \cos 0 + i \sin 0 )$$ 
C) ​   $$Z = 2 ( \cos 0 - i \sin 0 )$$ 
D) ​   $$Z = 2 ( \cos 0 + i \sin 0 )$$ 
E) ​   $$Z = 2 ( \cos 0 - i \sin 0 )$$

Question 11

Find all solutions to the following equation. $x ^ { 3 } - 216 = 0$

Accepted Answer

A) ​ $x = 6,6 + 6 i \sqrt { 3 } , 6 - 6 i \sqrt { 3 }$ 
B)  $x = 6,3 - 3 i \sqrt { 3 } , - 3 - 3 i \sqrt { 3 }$ 
C) ​ $x = 6 , - 3 - 3 i \sqrt { 3 } , - 3 + 3 i \sqrt { 3 }$ ​ 
D)  $x = - 6 i$ 
E)  $x = - 6$ 
A) ​ $x = 6,6 + 6 i \sqrt { 3 } , 6 - 6 i \sqrt { 3 }$ 
B)  $x = 6,3 - 3 i \sqrt { 3 } , - 3 - 3 i \sqrt { 3 }$ 
C) ​ $x = 6 , - 3 - 3 i \sqrt { 3 } , - 3 + 3 i \sqrt { 3 }$ ​ 
D)  $x = - 6 i$ 
E)  $x = - 6$

Question 12

Divide the complex numbers below and leave the result in trigonometric form. $$\frac { 5 \left( \cos 100 ^ { \circ } + i \sin 100 ^ { \circ } \right) } { 9 \left( \cos 120 ^ { \circ } + i \sin 120 ^ { \circ } \right) }$$ ​

Accepted Answer

A)  $\frac { 5 } { 9 } \left( \cos 220 ^ { \circ } + i \sin 220 ^ { \circ } \right)$ 
B) ​ $\frac { 5 } { 9 } \left( \cos 340 ^ { \circ } + i \sin 340 ^ { \circ } \right)$ 
C) ​ $45 \left( \cos 220 ^ { \circ } + i \sin 220 ^ { \circ } \right)$ 
D) ​ $\frac { 5 } { 9 } \left( \cos 340 ^ { \circ } + i \sin 220 ^ { \circ } \right)$ 
E) ​ $45 \left( \cos 340 ^ { \circ } + i \sin 340 ^ { \circ } \right)$ 
A)  $\frac { 5 } { 9 } \left( \cos 220 ^ { \circ } + i \sin 220 ^ { \circ } \right)$ 
B) ​ $\frac { 5 } { 9 } \left( \cos 340 ^ { \circ } + i \sin 340 ^ { \circ } \right)$ 
C) ​ $45 \left( \cos 220 ^ { \circ } + i \sin 220 ^ { \circ } \right)$ 
D) ​ $\frac { 5 } { 9 } \left( \cos 340 ^ { \circ } + i \sin 220 ^ { \circ } \right)$ 
E) ​ $45 \left( \cos 340 ^ { \circ } + i \sin 340 ^ { \circ } \right)$

Question 13

Perform the indicated operation using the standard form.​ $$- 6 i ( 1 + i )$$ ​

Accepted Answer

A)  $- 6 i ( 1 + i ) = 6 - 6 i$ 
B) ​ $$- 6 i ( 1 + i ) = 12 - 6 i$$ 
C) ​ $$- 6 i ( 1 + i ) = 6 + 12 i$$ 
D) ​ $- 6 i ( 1 + i ) = 6 - 12 i$ 
E) ​ $- 6 i ( 1 + i ) = 6 + 6 i$ 
A)  $- 6 i ( 1 + i ) = 6 - 6 i$ 
B) ​ $$- 6 i ( 1 + i ) = 12 - 6 i$$ 
C) ​ $$- 6 i ( 1 + i ) = 6 + 12 i$$ 
D) ​ $- 6 i ( 1 + i ) = 6 - 12 i$ 
E) ​ $- 6 i ( 1 + i ) = 6 + 6 i$

Question 14

Use DeMoivre's Theorem to find the indicated power of the complex number.Write the result in standard form. $- 7 ( \sqrt { 3 } + i ) ^ { 5 }$

Accepted Answer

A)  $112 \sqrt { 3 } - 112 i$ 
B)  $7 \sqrt { 3 } + 7 i$ 
C)  $- 112 \sqrt { 3 } + 112 i$ 
D)  $7 + 7 \sqrt { 3 } i$ 
E) ​ $112 \sqrt { 3 } + 112 i$ 
A)  $112 \sqrt { 3 } - 112 i$ 
B)  $7 \sqrt { 3 } + 7 i$ 
C)  $- 112 \sqrt { 3 } + 112 i$ 
D)  $7 + 7 \sqrt { 3 } i$ 
E) ​ $112 \sqrt { 3 } + 112 i$

Question 15

Use a graphing utility to represent the complex number in standard form.Round your answer to 4 decimal places.​ $$9 \left( \cos 62 ^ { \circ } + i \sin 62 ^ { \circ } \right)$$ ​

Accepted Answer

A) 7.9465 + 4.2252i 
B) 4.2252 + 7.9465i 
C) 4.2252 - 7.9465i 
D) 7.9465 - 4.2252i 
E) None of the above 
A) 7.9465 + 4.2252i 
B) 4.2252 + 7.9465i 
C) 4.2252 - 7.9465i 
D) 7.9465 - 4.2252i 
E) None of the above

Question 16

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

Accepted Answer

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

Question 17

Perform the indicated operation using the standard form.​ $$( \sqrt { 7 } + i ) ( 1 + i )$$ ​

Accepted Answer

A)  $( \sqrt { 7 } + i ) ( 1 + i ) \approx 1 + i$ 
B) ​ $( \sqrt { 7 } + i ) ( 1 + i ) \approx 3.646 - 1.646 i$ 
C) ​ $( \sqrt { 7 } + i ) ( 1 + i ) \approx 1.646 - 3.646 i$ 
D) ​ $( \sqrt { 7 } + i ) ( 1 + i ) \approx 1.646 + 3.646 i$ 
E) ​ $( \sqrt { 7 } + i ) ( 1 + i ) \approx 3.646 + 1.646 i$ 
A)  $( \sqrt { 7 } + i ) ( 1 + i ) \approx 1 + i$ 
B) ​ $( \sqrt { 7 } + i ) ( 1 + i ) \approx 3.646 - 1.646 i$ 
C) ​ $( \sqrt { 7 } + i ) ( 1 + i ) \approx 1.646 - 3.646 i$ 
D) ​ $( \sqrt { 7 } + i ) ( 1 + i ) \approx 1.646 + 3.646 i$ 
E) ​ $( \sqrt { 7 } + i ) ( 1 + i ) \approx 3.646 + 1.646 i$

Question 18

Multiply the complex numbers below and leave the result in trigonometric form. $$\left[ 0.1 \left( \cos 260 ^ { \circ } + i \sin 260 ^ { \circ } \right) \right] \left[ 0.9 \left( \cos 220 ^ { \circ } + i \sin 220 ^ { \circ } \right) \right]$$ ​

Accepted Answer

A)  $0.09 \left( \cos 120 ^ { \circ } + i \sin 120 ^ { \circ } \right)$ 
B) ​ $0.09 \left( \cos 120 ^ { \circ } + i \sin 40 ^ { \circ } \right)$ 
C) ​ $\cos 40 ^ { \circ } + i \sin 40 ^ { \circ }$ 
D) ​ $0.09 \left( \cos 40 ^ { \circ } + i \sin 40 ^ { \circ } \right)$ 
E) ​ $\cos 120 ^ { \circ } + i \sin 120 ^ { \circ }$ 
A)  $0.09 \left( \cos 120 ^ { \circ } + i \sin 120 ^ { \circ } \right)$ 
B) ​ $0.09 \left( \cos 120 ^ { \circ } + i \sin 40 ^ { \circ } \right)$ 
C) ​ $\cos 40 ^ { \circ } + i \sin 40 ^ { \circ }$ 
D) ​ $0.09 \left( \cos 40 ^ { \circ } + i \sin 40 ^ { \circ } \right)$ 
E) ​ $\cos 120 ^ { \circ } + i \sin 120 ^ { \circ }$

Question 19

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

Accepted Answer

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

Question 20

Find the trigonometric form of $- 6 - 6 \sqrt { 3 } i$ .

Accepted Answer

A)  $12 \left( \cos \frac { 4 \pi } { 3 } + i \sin \frac { 4 \pi } { 3 } \right)$ 
B)  $6 \left( \cos \frac { 4 \pi } { 3 } + i \sin \frac { 4 \pi } { 3 } \right)$ 
C)  $12 \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$ 
D)  $12 \left( \cos \frac { 7 \pi } { 6 } + i \sin \frac { 7 \pi } { 6 } \right)$ 
E)  $6 \sqrt { 2 } \left( \cos \frac { 7 \pi } { 6 } + i \sin \frac { 7 \pi } { 6 } \right)$ 
A)  $12 \left( \cos \frac { 4 \pi } { 3 } + i \sin \frac { 4 \pi } { 3 } \right)$ 
B)  $6 \left( \cos \frac { 4 \pi } { 3 } + i \sin \frac { 4 \pi } { 3 } \right)$ 
C)  $12 \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$ 
D)  $12 \left( \cos \frac { 7 \pi } { 6 } + i \sin \frac { 7 \pi } { 6 } \right)$ 
E)  $6 \sqrt { 2 } \left( \cos \frac { 7 \pi } { 6 } + i \sin \frac { 7 \pi } { 6 } \right)$

Exam 40: Trigonometric Form of a Complex Number

Find the trigonometric form of the complex number shown below. 6i6 i6i

Find the trigonometric form of the complex number shown below. ​ ​-8

Write the complex number shown below in trigonometric form.

Find the standard form of the complex number shown below. 3(cos⁡7π6+isin⁡7π6)3 \left( \cos \frac { 7 \pi } { 6 } + i \sin \frac { 7 \pi } { 6 } \right)3(cos67π​+isin67π​)

Find the product (−5+5i)(7−7i)( - 5 + 5 i ) ( 7 - 7 i )(−5+5i)(7−7i) using trigonometric forms.Leave the result in trigonometric form.

Plot the complex number and find its absolute value. ​ -5 + 2i ​

Perform the indicated operation in trigonometric form.Write the solution in standard form rounded to four decimal places. 4+i38−3i\frac { 4 + i \sqrt { 3 } } { 8 - 3 i }8−3i4+i3​​ ​

Represent the complex number below graphically. 3+i\sqrt { 3 } + i3​+i

Plot the complex number and find its absolute value. ​ -5 + 9i ​

Represent the complex number graphically. ​ 2 ​

Find all solutions to the following equation. x3−216=0x ^ { 3 } - 216 = 0x3−216=0

Perform the indicated operation using the standard form.​ −6i(1+i)- 6 i ( 1 + i )−6i(1+i) ​

Use DeMoivre's Theorem to find the indicated power of the complex number.Write the result in standard form. −7(3+i)5- 7 ( \sqrt { 3 } + i ) ^ { 5 }−7(3​+i)5

Use a graphing utility to represent the complex number in standard form.Round your answer to 4 decimal places.​ 9(cos⁡62∘+isin⁡62∘)9 \left( \cos 62 ^ { \circ } + i \sin 62 ^ { \circ } \right)9(cos62∘+isin62∘) ​

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

Perform the indicated operation using the standard form.​ (7+i)(1+i)( \sqrt { 7 } + i ) ( 1 + i )(7​+i)(1+i) ​

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

Find the trigonometric form of −6−63i- 6 - 6 \sqrt { 3 } i−6−63​i .

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

Find the trigonometric form of the complex number shown below. $6 i$

Find the trigonometric form of the complex number shown below. -8

Find the standard form of the complex number shown below. $3 \left( \cos \frac { 7 \pi } { 6 } + i \sin \frac { 7 \pi } { 6 } \right)$

Find the product $( - 5 + 5 i ) ( 7 - 7 i )$ using trigonometric forms.Leave the result in trigonometric form.

Plot the complex number and find its absolute value. -5 + 2i

Perform the indicated operation in trigonometric form.Write the solution in standard form rounded to four decimal places. $\frac { 4 + i \sqrt { 3 } } { 8 - 3 i }$

Represent the complex number below graphically. $\sqrt { 3 } + i$ $Represent the complex number below graphically. \sqrt { 3 } + i$

Plot the complex number and find its absolute value. -5 + 9i

Represent the complex number graphically. 2

Find all solutions to the following equation. $x ^ { 3 } - 216 = 0$

Perform the indicated operation using the standard form. $- 6 i ( 1 + i )$

Use DeMoivre's Theorem to find the indicated power of the complex number.Write the result in standard form. $- 7 ( \sqrt { 3 } + i ) ^ { 5 }$

Use a graphing utility to represent the complex number in standard form.Round your answer to 4 decimal places. $9 \left( \cos 62 ^ { \circ } + i \sin 62 ^ { \circ } \right)$

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

Perform the indicated operation using the standard form. $( \sqrt { 7 } + i ) ( 1 + i )$

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

Find the trigonometric form of $- 6 - 6 \sqrt { 3 } i$ .