Calculus questions on trigonometric functions
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.LarPreCalcRMRPAlt6 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.LarPreCalcRMRPAlt6 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.LarPreCalcRMRPAlt6 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.LarPreCalcRMRPAlt6 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.LarPreCalcRMRPAlt6 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.LarPreCalcRMRPAlt6 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.LarPreCalcRMRPAlt6 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.LarPreCalcRMRPAlt6 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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