Project #52779 - Trig6

 

Answer questions 1-7. Provide detailed work illustrating how you arrived at your solution.

 

  1. Determine if the following are true statements and explain your reasoning.

 

Some complex numbers are irrational numbers.

 

The product (2 + i)(2 – i) cannot be a real number.

 

The imaginary number I raised to any exponent is equal to one of the following 1, -1 I or –i.

 

 

 

2) Express the following in the standard form for a complex number

 

https://content.grantham.edu/at/MA111/New_2013/Assignment_Images/w6_a1_1.png

 

3) Express the following in the standard form for a complex number

 

https://content.grantham.edu/at/MA111/New_2013/Assignment_Images/w6_a1_2.png

 

4) Write the complex number in standard form: https://content.grantham.edu/at/MA111/New_2013/Assignment_Images/w6_a1_3.png

 

5) Using DeMoivre’s Theorem solve: z2 + 100 = 0

 

6) Using DeMoivre’s Theorem solve: z3 - 64 = 0

 

7) Express the complex number z = -1 + 2i in trigonometric form.

 

 

 

 

 

Work is not required to be shown for the next 20 questions.

 

Question 1

 

  1. Find the product of the complex numbers.z1 = 7(cos (π/4) + i sin (π /4))z2 = 3(cos (π /6) + i sin (π /6))

 

A.

10(cos (π/12) + i sin (π/12))

B.

21(cos (5 π/12) + i sin (5 π/12))

C.

10(cos (5π /12) + i sin (5π /12))

D.

21(cos (π/12) + i sin (π/12))

 

Question 2

 

  1. Perform the indicated operation.(2 - 5i) + (8 + 7i)

 

A.

-6 + 12i

B.

10 + 2i

C.

10 - 2i

D.

-10 - 2i

 

Question 3

 

  1. Use DeMoivre's Theorem to find the indicated power of the complex number. [2(cos 15° + i sin 15°)]4

 

A.

16i

B.

 https://content.grantham.edu/at/MA111/New_2013/Assessment_Images/Week_6/w6_assessment_18_04.png

C.

8 + 8i

D.

 https://content.grantham.edu/at/MA111/New_2013/Assessment_Images/Week_6/w6_assessment_18_03.png

 

Question 4

 

  1. Find the complex square roots of 49(cos 30° + i sin 30°)

 

A.

7(cos 15° + i sin 15°), 105(cos 195° + i sin 195°)

B.

7(cos 30° + i sin 30°), -7(cos 105° + i sin 105°)

C.

7(cos 15° + i sin 15°), 7(cos 195° + i sin 195°)

D.

7(cos 30° + i sin 30°), 7(cos 105° + i sin 105°)

 

Question 5

 

  1.  Find the product and write the result in standard form.

 

(2 - 6i)2

 

A.

-32

B.

4 - 24i + 36i2

C.

-32 - 24i

D.

40 - 24i

 

Question 6

 

  1. Perform the indicated operation.(4 + 5i) - (-7 + i)

 

A.

11 + 4i

B.

-3 + 6i

C.

11 - 4i

D.

-11 - 4i

 

Question 7

 

  1. Write the complex number 6 + 8i in trigonometric form.

 

A.

10(cos 126.9° + i sin 126.9°)

B.

10(cos 233.1° + i sin 233.1°)

C.

10(cos 53.1° + i sin 53.1°)

D.

10(cos 306.9° + i sin 306.9°)

 

Question 8

 

  1.  Write the complex number in standard form 3(cos 225° + i sin 225°).

 

A.

 https://content.grantham.edu/at/MA111/New_2013/Assessment_Images/Week_6/w6_assessment_13_01.png

B.

 https://content.grantham.edu/at/MA111/New_2013/Assessment_Images/Week_6/w6_assessment_13_05.png

C.

 https://content.grantham.edu/at/MA111/New_2013/Assessment_Images/Week_6/w6_assessment_13_03.png

D.

 https://content.grantham.edu/at/MA111/New_2013/Assessment_Images/Week_6/w6_assessment_13_04.png

E.

 https://content.grantham.edu/at/MA111/New_2013/Assessment_Images/Week_6/w6_assessment_13_02.png

 

Question 9

 

  1. Perform the indicated operation.5i - (-5 - i)

 

A.

5 + 6i

B.

-5 + 4i

C.

-5 - 6i

D.

5 - 4i

 

Question 10

 

  1. Use DeMoivre's Theorem to find the indicated power of the complex number. (1 - i)10

 

A.

32

B.

32 - 32i

C.

-32 + 32i

D.

-32i

 

Question 11

 

  1. Find the absolute value of the complex number. z = -7

 

A.

0

B.

-7

C.

14

D.

7

 

Question 12

 

  1.  https://content.grantham.edu/at/MA111/New_2013/Assessment_Images/Week_6/w6_assessment_10_00.png

 

A.

 https://content.grantham.edu/at/MA111/New_2013/Assessment_Images/Week_6/w6_assessment_10_02.png

B.

 https://content.grantham.edu/at/MA111/New_2013/Assessment_Images/Week_6/w6_assessment_10_04.png

C.

 https://content.grantham.edu/at/MA111/New_2013/Assessment_Images/Week_6/w6_assessment_10_03.png

D.

 https://content.grantham.edu/at/MA111/New_2013/Assessment_Images/Week_6/w6_assessment_10_01.png

 

Question 13

 

  1. Find the product and write the result in standard form. -2i(7i - 4)

 

A.

8i - 14i2

B.

8i + 14i2

C.

14 + 8i

D.

-14 + 8i

 

Question 14

 

  1.  Find the absolute value of the complex number z = -11 - 6i

 

A.

 https://content.grantham.edu/at/MA111/New_2013/Assessment_Images/Week_6/w6_assessment_07_02.png

B.

 https://content.grantham.edu/at/MA111/New_2013/Assessment_Images/Week_6/w6_assessment_07_03.png

C.

 https://content.grantham.edu/at/MA111/New_2013/Assessment_Images/Week_6/w6_assessment_07_01.png

D.

 https://content.grantham.edu/at/MA111/New_2013/Assessment_Images/Week_6/w6_assessment_07_04.png

 

Question 15

 

  1. Find the product and write the result in standard form (4 + 5i)(2 - 8i)

 

A.

40i2 - 22i + 8

B.

48 + 22i

C.

48 - 22i

D.

-32 + 42i

 

Question 16

 

  1. Find the product of the complex numbers.z1 = 5(cos 20° + i sin 20°)z2 = 4(cos 10° + i sin 10°)

 

A.

9(cos 30° + i sin 30°)

B.

20(cos 10° + i sin 10°)

C.

20(cos 30° + i sin 30°)

D.

9(-cos 200° - i sin 200°)

 

Question 17

 

  1. Find the complex cube roots of 343(cos 291° + i sin 291°)

 

A.

7(cos 97° + i sin 97°), 7(cos217° + i sin 217°), 7(cos 337° + i sin 337°)

B.

7(cos 97° - i sin 97°), 7(cos217° - i sin 217°), 7(cos 337° - i sin 337°)

C.

-7(cos 97° + i sin 97°), 7(cos 137° + i sin 137°), -7(cos 177° + i sin 177°)

D.

-7(cos 97° + i sin 97°), 7(cos 217° + i sin 217°), -7(cos 337° + i sin 337°)

E.

7(cos 97° + i sin 97°), 7(cos 137° + i sin 137°), 7(cos 177° + i sin 177°)

 

Question 18

 

  1. Find the quotient (z1/z2) of the complex numbers.

 

z1 = 5(cos 200° + i sin 200°)

 

z2 = 4(cos 50° + i sin 50°)

 

A.

(5/4)(cos 150° - i sin 150°)

B.

(5/4)(cos 150° + i sin 150°)

C.

(5/4)(cos 250° + i sin 250°)

D.

(5/4)(sin 150° + i cos 150°)

 

Question 19

 

  1. Write the complex number 6i in trigonometric form.

 

A.

6(cos 270° + i sin 270°)

B.

6(cos 180° + i sin 180°)

C.

6(cos 0° + i sin 0°)

D.

6(cos 90° + i sin 90°)

 

Question 20

 

  1. Find the absolute value of the complex number z = -8 - 12i

 

A.

2i√13

B.

2

C.

4i√13

D.

4√13

 

Subject Mathematics
Due By (Pacific Time) 12/29/2014 08:00 am
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