Description
For a positive integer
n | r |
θ + 2πk |
n |
θ + 2πk |
n |
Consider the following.
Cube roots of −4
2 |
(a) Use the formula to find the indicated roots of the complex number. (Enter your answers in trigonometric form.)
k = 0: | |
k = 1: |
|
k = 2: |
|
(b) Represent each of the roots graphically.
|
(c) Write each of the roots in standard form. (Round your answers to four decimal places.)
k = 0: |
|
k = 1: |
|
k = 2: |
|
2.–/5.55 pointsLarPreCalcRMRPAlt6 7.5.068.My Notes
Question Part |
Points |
Perform the operation and leave the result in trigonometric form.
3 |
2 |
π |
6 |
π |
6 |
π |
4 |
π |
4 |
3.–/5.55 pointsLarPreCalcRMRPAlt6 7.5.076.My Notes
Question Part |
Points |
Perform the operation and leave the result in trigonometric form.
cos
| ||||||||
cos π + i sin π |
4.–/5.55 pointsLarPreCalcRMRPAlt6 7.5.078.My Notes
Question Part |
Points |
Perform the operation and leave the result in trigonometric form.
4(cos 60° + i sin 60°) |
5(cos 100° + i sin 100°) |
5.–/5.55 pointsLarPreCalcRMRPAlt6 7.5.074.My Notes
Question Part |
Points |
Perform the operation and leave the result in trigonometric form. (Let 0 ≤ θ < 2π.)
3(cos(3.6) + i sin(3.6)) |
2(cos(1.4) + i sin(1.4)) |
6.–/5.55 pointsLarPreCalcRMRPAlt6 7.5.070.MI.My Notes
Question Part |
Points |
Perform the operation and leave the result in trigonometric form. (Enter your angles in degrees between 0° and 360°.)
1 |
3 |
4 |
5 |
7.–/5.55 pointsLarPreCalcRMRPAlt6 7.5.048.MI.My Notes
Question Part |
Points |
Find the standard form of the complex number. Then represent the complex number graphically.5(cos 45° + i sin 45°)
|
8.–/5.55 pointsLarPreCalcRMRPAlt6 7.5.034.My Notes
Question Part |
Points |
Represent the complex number graphically.
7 |
2 |
3 |
|
Write the trigonometric form of the number.
(Let 0 ≤ θ < 2π.)
z =
9.–/5.55 pointsLarPreCalcRMRPAlt6 7.5.110.My Notes
Question Part |
Points |
Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form.(3 − 2i)8
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