Question 1 of 20

0.0/ 5.0 Points 
Write the vector v in terms of i and j whose magnitude and direction angle θ are given.
= 8, θ = 30°

A. v = 4_{}i + 4j 


B. v = 4_{}i + 4_{}j 


C. v = 4_{}i + 4j 


D. v = 4i + 4_{}j 


Question 2 of 20

0.0/ 5.0 Points 
Select the representation that does not change the location of the given point. (4, 110°)

A. (4, 470)° 


B. (4, 290)° 


C. (4, 200)° 


D. (4, 470)° 


Question 3 of 20

0.0/ 5.0 Points 
Find the quotient _{}of the complex numbers. Leave answer in polar form.
z1 = _{}
z2 =

Question 4 of 20

0.0/ 5.0 Points 

Question 5 of 20

5.0/ 5.0 Points 
Polar coordinates of a point are given. Find the rectangular coordinates of the point.

A. (1.6, 1.3) 


B. (1.6, 1.3) 


C. (1.3, 1.6) 


D. (1.3, 1.6) 


Question 6 of 20

0.0/ 5.0 Points 
Find the work done by a force of 4 pounds acting in the direction of 41° to the horizontal in moving an object 5 feet from (0, 0) to (5, 0).

A. 13.1 ftlb 


B. 16.2 ftlb 


C. 15.1 ftlb 


D. 30.2 ftlb 


Question 7 of 20

0.0/ 5.0 Points 
Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. a = 6, c = 11, B = 109°

A. b = 14.1, A = 24°, C = 47° 


B. b = 19.9, A = 22°, C = 49° 


C. b = 17, A = 26°, C = 45° 


D. no triangle 


Question 8 of 20

0.0/ 5.0 Points 
Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. B = 15° C = 113° b = 49

A. A = 50°, a = 176.3, c = 151.2 


B. A = 52°, a = 149.2, c = 174.3 


C. A = 52°, a = 151.2, c = 176.3 


D. A = 50°, a = 174.3, c = 149.2 


Question 9 of 20

0.0/ 5.0 Points 
Find all the complex roots. Write the answer in the indicated form. The complex cube roots of 27(cos 234° + i sin 234°) (polar form)

A. 3(cos 78° + i sin 78°), 3(cos 198° + i sin 198°), 3(cos 318° + i sin 318°) 


B. 3(cos 78° + i sin 78°), 3(cos 118° + i sin 118°), 3(cos 158° + i sin 158°) 


C. 3(cos 78° + i sin 78°), 3(cos 118° + i sin 118°), 3(cos 158° + i sin 158°) 


D. 3(cos 78° + i sin 78°), 3(cos198° + i sin 198°), 3(cos 318° + i sin 318°) 


Question 10 of 20

5.0/ 5.0 Points 
Find the specified vector or scalar.
u = 4i + 1j and v = 4i + 1j; Find .

A. 


B. 8 


C. 5 


D. 2 


Question 11 of 20

5.0/ 5.0 Points 
Use the dot product to determine whether the vectors are parallel, orthogonal, or neither. v = j, w = 4i

A. orthogonal 


B. parallel 


C. neither 


Question 12 of 20

0.0/ 5.0 Points 
Write the complex number in polar form. Express the argument in degrees. 4i

A. 4(cos 0° + i sin 0°) 


B. 4(cos 270° + i sin 270°) 


C. 4(cos 90° + i sin 90°) 


D. 4(cos 180° + i sin 180°) 


Question 13 of 20

0.0/ 5.0 Points 
The wind is blowing at 10 knots. Sailboat racers look for a sailing angle to the 10knot wind that produces maximum sailing speed. This situation is now represented by the polar graph in the figure shown below. Each point (r, θ) on the graph gives the sailing speed, r, in knots, at an angle θ to the 10knot wind. What is the speed to the nearest knot, of the sailboat sailing at 120° angle to the wind?

A. 8 knots 


B. 9 knots 


C. 7 knots 


D. 10 knots 


Question 14 of 20

0.0/ 5.0 Points 
Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. a = 7, b = 7, c = 5

A. A = 70°, B = 70°, C = 40° 


B. A = 69°, B = 69°, C = 42° 


C. A = 42°, B = 69°, C = 69° 


D. A = 69°, B = 42°, C = 69° 


Question 15 of 20

0.0/ 5.0 Points 
Plot the complex number. 2 + i

Question 16 of 20

0.0/ 5.0 Points 
Find the magnitude and direction angle θ, to the nearest tenth of a degree, for the given vector v. v = 4i – 3j

A. 5; 233.1° 


B. 7; 216.9° 


C. 5; 216.9° 


D. 5; 36.9° 


Question 17 of 20

0.0/ 5.0 Points 
Find the quotient of the complex numbers. Leave answer in polar form.
z1 =
z2 =

Question 18 of 20

0.0/ 5.0 Points 
Graph the polar equation.
r = 2 + 2sin θ

Question 19 of 20

0.0/ 5.0 Points 
Polar coordinates of a point are given. Find the rectangular coordinates of the point. (5, 180°)

A. (5, 0) 


B. (0, 5) 


C. (0, 5) 


D. (5, 0) 


Question 20 of 20

0.0/ 5.0 Points 
Plot the complex number.
5_{}– 5i
