Question 1

Find the product of the given complex number and its conjugate.
-

Accepted Answer

A)    
B)    
C)  25 
D)  5 
A)    
B)    
C)  25 
D)  5

Question 2

Solve.
-Two forces of 75 and 30 N (newtons) act on an object at right angles. Find the magnitude of the resultant and the angle that it makes with the larger force.

Accepted Answer

A)  81 N, 22° 
B)  81 N, 68° 
C)  6525 N, 22° 
D)  81 N, 17° 
A)  81 N, 22° 
B)  81 N, 68° 
C)  6525 N, 22° 
D)  81 N, 17°

Question 3

Solve the triangle. If there is more than one triangle with the given parts, give both solutions.
-  = 16.31° b = 15.45
A = 18.34

Accepted Answer

A)  No solution 
B)    
C)    
D)    
A)  No solution 
B)    
C)    
D)

Question 4

Perform the indicated operation. Use the form for vectors. -u = <13, -14> and v = <-9, -13>; Find u ·v.

Accepted Answer

A)  -299 
B)  -117 
C)  182 
D)  65 
A)  -299 
B)  -117 
C)  182 
D)  65

Question 5

Graph the complex number.
-

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 6

Find the component form for the vector with the given magnitude and direction angle   . Round values to the nearest
tenth.
-

Accepted Answer

A)  100.6, 64.6 
B)  -100.6, -64.6 
C)  -64.6, -100.6 
D)  64.6, 100.6 
A)  100.6, 64.6 
B)  -100.6, -64.6 
C)  -64.6, -100.6 
D)  64.6, 100.6

Question 7

Write the complex number in the form a + bi.
-3(cos 270° + i sin 270°)

Accepted Answer

A)  -3i 
B)  3 
C)  3i 
D)  -3 
A)  -3i 
B)  3 
C)  3i 
D)  -3

Question 8

State if the vectors a and b are perpendicular, parallel, or neither. If a and b are parallel, state whether they point in the
same direction or in opposite directions.
-a = 10, 0 , b = 0, -2

Accepted Answer

A)  Parallel, opposite directions 
B)  Parallel, same direction 
C)  Perpendicular 
D)  Neither 
A)  Parallel, opposite directions 
B)  Parallel, same direction 
C)  Perpendicular 
D)  Neither

Question 9

Find the indicated roots. Write the answer in trigonometric form.
-Fourth roots of 256(cos 320° + i sin 320°)

Accepted Answer

A)  4(cos 320° + i sin 320°), 4(cos 410° + i sin 410°), 4(cos 500° + i sin 500°), 4(cos 230° + i sin 230°) 
B)  4(cos 80° + i sin 80°), 4(cos 170° + i sin 170°), 4(cos 260° + i sin 260°), 4(cos 350° + i sin 350°) 
C)  4(cos 80° + i sin 80°), 4(cos 170° + i sin 170°), 4(cos 340° + i sin 340°), 4(cos 70° + i sin 70°) 
D)  4(cos 160° + i sin 160°), 4(cos 250° + i sin 250°), 4(cos 340° + i sin 340°), 4(cos 70° + i sin 70°) 
A)  4(cos 320° + i sin 320°), 4(cos 410° + i sin 410°), 4(cos 500° + i sin 500°), 4(cos 230° + i sin 230°) 
B)  4(cos 80° + i sin 80°), 4(cos 170° + i sin 170°), 4(cos 260° + i sin 260°), 4(cos 350° + i sin 350°) 
C)  4(cos 80° + i sin 80°), 4(cos 170° + i sin 170°), 4(cos 340° + i sin 340°), 4(cos 70° + i sin 70°) 
D)  4(cos 160° + i sin 160°), 4(cos 250° + i sin 250°), 4(cos 340° + i sin 340°), 4(cos 70° + i sin 70°)

Question 10

Solve.
-The sides of a parallelogram are 12 ft and 14 ft. One angle is 40° while another angle is 140°. Find the lengths of the diagonals of the parallelogram (to the nearest tenth of a foot).

Accepted Answer

A)  16.8 ft and 9.1 ft 
B)  9.1 ft and 24.4 ft 
C)  14.5 ft and 21.6 ft 
D)  82.6 ft and 597.4 ft 
A)  16.8 ft and 9.1 ft 
B)  9.1 ft and 24.4 ft 
C)  14.5 ft and 21.6 ft 
D)  82.6 ft and 597.4 ft

Question 11

Find the absolute value of the complex number.
-2

Accepted Answer

A)  2i 
B)  2 
C)  4 
D)    
A)  2i 
B)  2 
C)  4 
D)

Question 12

Solve the equation. Write the answer in a + bi form.
-z4 + 16 = 0

Accepted Answer

A)  2 + i, 2 - i, -2 + i, -2 - i 
B)    
C)  1 + i, 1 - i, -1 + i, -1 - i 
D)    
A)  2 + i, 2 - i, -2 + i, -2 - i 
B)    
C)  1 + i, 1 - i, -1 + i, -1 - i 
D)

Find the product of the given complex number and its conjugate. -

Solve. -Two forces of 75 and 30 N (newtons) act on an object at right angles. Find the magnitude of the resultant and the angle that it makes with the larger force.

Solve the triangle. If there is more than one triangle with the given parts, give both solutions. - = 16.31° b = 15.45 A = 18.34

Perform the indicated operation. Use the form <a, b> for vectors. -u = <13, -14> and v = <-9, -13>; Find u ·v.

Graph the complex number. -

Find the component form for the vector with the given magnitude and direction angle . Round values to the nearest tenth. -

Write the complex number in the form a + bi. -3(cos 270° + i sin 270°)

State if the vectors a and b are perpendicular, parallel, or neither. If a and b are parallel, state whether they point in the same direction or in opposite directions. -a = 10, 0 , b = 0, -2

Find the indicated roots. Write the answer in trigonometric form. -Fourth roots of 256(cos 320° + i sin 320°)

Solve. -The sides of a parallelogram are 12 ft and 14 ft. One angle is 40° while another angle is 140°. Find the lengths of the diagonals of the parallelogram (to the nearest tenth of a foot).

Find the absolute value of the complex number. -2

Solve the equation. Write the answer in a + bi form. -z4 + 16 = 0

Equations, Inequalities, and Modeling

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

The Trigonometric Functions

Trigonometric Identities and Conditional Equations

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The Conic Sections

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Exam 7: Applications of Trigonometry