Multi Choice Problems question 1to 20

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

= 8, θ = 30°

	A. v = -4i + 4j
	B. v = 4i + 4j
	C. v = 4i + 4j
	D. v = 4i + 4j

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)°

Find the quotient of the complex numbers. Leave answer in polar form.

z1 =

z2 =

	A.
	B.
	C.
	D.

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 = 3i + j
	D. u = i + j

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)

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

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

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

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°)

Find the specified vector or scalar.

u = -4i + 1j and v = 4i + 1j; Find .

	A.
	B. 8
	C. 5
	D. 2

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

	A. orthogonal
	B. parallel
	C. neither

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°)

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

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°

Plot the complex number. 2 + i

	A.
	B.
	C.
	D.

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°

Find the quotient of the complex numbers. Leave answer in polar form.

z1 = 
z2 =

	A.
	B.
	C.
	D.

Graph the polar equation.

r = 2 + 2sin θ

	A.
	B.
	C.
	D.

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)

Plot the complex number.

-5– 5i

	A.
	B.
	C.
	D.