Question 1

Find the trigonometric form of $$- 14 \sqrt { 3 } + 14 i$$ . ​

Accepted Answer

A) ​ $$14 \left( \cos \frac { 5 \pi } { 6 } + i \sin \frac { 5 \pi } { 6 } \right)$$ 
B) ​ $196 \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$ 
C) ​ $14 \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$ 
D) ​ $28 \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$ 
E) ​ $28 \left( \cos \frac { 5 \pi } { 6 } + i \sin \frac { 5 \pi } { 6 } \right)$ 
A) ​ $$14 \left( \cos \frac { 5 \pi } { 6 } + i \sin \frac { 5 \pi } { 6 } \right)$$ 
B) ​ $196 \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$ 
C) ​ $14 \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$ 
D) ​ $28 \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$ 
E) ​ $28 \left( \cos \frac { 5 \pi } { 6 } + i \sin \frac { 5 \pi } { 6 } \right)$

Question 2

Find the absolute value of the complex number $$8 + 2 i$$ . ​

Accepted Answer

A) ​ $\sqrt { 10 }$ 
B) ​ $3 \sqrt { 10 }$ 
C) ​68 
D) ​ $4 \sqrt { 10 }$ 
E) ​ $2 \sqrt { 17 }$ 
A) ​ $\sqrt { 10 }$ 
B) ​ $3 \sqrt { 10 }$ 
C) ​68 
D) ​ $4 \sqrt { 10 }$ 
E) ​ $2 \sqrt { 17 }$

Question 3

Perform the operation and leave the result in trigonometric form.​ $$\frac { \cos \pi + i \sin \pi } { \cos ( \pi / 9 ) + i \sin ( \pi / 9 ) }$$ ​

Accepted Answer

A)  $\cos \frac { 9 \pi } { 8 } - i \sin \frac { 9 \pi } { 8 }$ 
B) ​ $\cos \frac { 9 \pi } { 8 } - \sin \frac { 9 \pi } { 8 }$ 
C) ​ $\cos \frac { 8 \pi } { 9 } + i \sin \frac { 8 \pi } { 9 }$ 
D) ​ $\cos \frac { 8 \pi } { 9 } - i \sin \frac { 8 \pi } { 9 }$ 
E) ​ $\cos \frac { 9 \pi } { 8 } + i \sin \frac { 9 \pi } { 8 }$ 
A)  $\cos \frac { 9 \pi } { 8 } - i \sin \frac { 9 \pi } { 8 }$ 
B) ​ $\cos \frac { 9 \pi } { 8 } - \sin \frac { 9 \pi } { 8 }$ 
C) ​ $\cos \frac { 8 \pi } { 9 } + i \sin \frac { 8 \pi } { 9 }$ 
D) ​ $\cos \frac { 8 \pi } { 9 } - i \sin \frac { 8 \pi } { 9 }$ 
E) ​ $\cos \frac { 9 \pi } { 8 } + i \sin \frac { 9 \pi } { 8 }$

Question 4

Find the trigonometric form of $- 5 + 5 \sqrt { 3 } i$ . ​

Accepted Answer

A)  $5 \sqrt { 2 } \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$ 
B) ​ $5 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$ 
C) ​ $$5 \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$$ 
D) ​ $$10 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$$ 
E) ​ $10 \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$ 
A)  $5 \sqrt { 2 } \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$ 
B) ​ $5 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$ 
C) ​ $$5 \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$$ 
D) ​ $$10 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$$ 
E) ​ $10 \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$

Exam 40: Trigonometric Form of a Complex Number

Find the trigonometric form of −143+14i- 14 \sqrt { 3 } + 14 i−143​+14i . ​

Find the absolute value of the complex number 8+2i8 + 2 i8+2i . ​

Perform the operation and leave the result in trigonometric form.​ cos⁡π+isin⁡πcos⁡(π/9)+isin⁡(π/9)\frac { \cos \pi + i \sin \pi } { \cos ( \pi / 9 ) + i \sin ( \pi / 9 ) }cos(π/9)+isin(π/9)cosπ+isinπ​ ​

Find the trigonometric form of −5+53i- 5 + 5 \sqrt { 3 } i−5+53​i . ​

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Find the trigonometric form of $- 14 \sqrt { 3 } + 14 i$ .

Find the absolute value of the complex number $8 + 2 i$ .

Perform the operation and leave the result in trigonometric form. $\frac { \cos \pi + i \sin \pi } { \cos ( \pi / 9 ) + i \sin ( \pi / 9 ) }$

Find the trigonometric form of $- 5 + 5 \sqrt { 3 } i$ .