# Write the vector v in terms of i and j whose magnitude and direction angle θ are given.

##### Question 1 of 20
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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
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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
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Find the quotient of the complex numbers. Leave answer in polar form.

z1 =  z2 =  A.  B.  C.  D.  ##### Question 4 of 20
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Find the unit vector that has the same direction as the vector v. v = 3i + j

A. u = i + j
B. u = i + j
C. u = 3 i + j
D. u = i + j
##### Question 5 of 20
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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
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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 ft-lb
B. 16.2 ft-lb
C. 15.1 ft-lb
D. 30.2 ft-lb
##### Question 7 of 20
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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
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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
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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
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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
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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
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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
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The wind is blowing at 10 knots. Sailboat racers look for a sailing angle to the 10-knot 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 10-knot 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
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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
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Plot the complex number. 2 + i

A. B. C. D. ##### Question 16 of 20
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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
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Find the quotient of the complex numbers. Leave answer in polar form.

z1 =  z2 =  A.  B.  C.  D.  ##### Question 18 of 20
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Graph the polar equation.

r = 2 + 2sin θ

A. B. C. D. ##### Question 19 of 20
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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

A. B. C. D.  Pages (550 words)
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