Complex numbers Questions and Answers

Complete the sentence below The graph of f k gk passes through the points 1 D 0 and 1 Simplify your answers

The graph of a function f is shown Use the graph to find f1 7 10 10 Ay X 2

Find a formula in terms of k for the entries of Ak where A is the diagonalizable matrix below A 19 18 20 19 00

3 Combine like terms in the expression below 3 2x 4 3x

4 Combine like terms in the expression below 2 4x 2 3 2x 6

4 Simplify by combining like terms 2 x 4x 5 3 x 3x 4

3 If 3x 4x 10 4x 6x 4 is rewritten in the form ax bx c what is the value of a a 3 b 7 c 3 d 12

2 Which of the following expressions is equivalent to 3 x 10x 4 3x 4 a 3x 18x 16 b 3x 42x 16 c 3x 42x 16 d 3x 18x 16

Exit Ticket 14 1 Which of the following expressions is equivalent to 2 2x 10 3 x 10 a 7x 10 b 7x50 c 7x 10 d x

Simplify the following trigonometric expression by following the indicated direction Multiply cos e cos 0 sin 0 1 sin 0 1 by sin 0 1 sin 0 1 Simplify your answer

Find the exact value of the logarithm without using a calcu log 12144

Use a calculator to evaluate the expression 10 In 1 9 In 20

11 2 3 2 5

12 4 3 1 2V

Suppose 1 2 lies on the terminal side of angle x when is drawn in standard position Find the following sin 2x cos 2x In which quadrant does the terminal side of angle 2x lie Answer 1 2 3 or 4 2

Solve the equation over the interval 0 2x then support your solutions graphically 2 cos 2x 2 cos x 0 Select the correct choice below and if necessary fill in the answer box to complete your choice O A 2 4x The solution set is 0 33 Use a comma to separate answers as needed Type exact answers using a as needed OB The solution is the empty set

Solve for exact solutions over the interval 0 2 cos2x 3 2 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The solution set is Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression Use a comma to separate answers as neede OB The solution set is

A die is rolled The set of equally likely outcomes is 1 2 3 4 5 6 Find the probability of getting a 6 1 Listen 0 6 6

Find the orders of all the nonzero elements of GF 3 x 2x 2

The ages of 25 patients who suffered strokes are as follows 69 72 46 81 45 50 57 61 48 56 77 58 74 73 80 47 53 60 58 46 61 66 55 79 84 Fill in the blanks in the grouped frequency distribution for the data belov Classes Frequency 45 49 50 54 55 59 60 64 65 69 70 74 75 79 80 84

Find the orders of all the nonzero elements of GF 3 x 2x 2

Solve the triangle with the given parts a 23 9 m b 13 3 m c 21 6 m What is the degree measure of angle A 82 8 Round to the nearest tenth as needed What is the degree measure of angle B Round to the nearest tenth as needed

se sin x 0 2938 cos x 0 9559 tan x 0 3074 sin x 0 2938 cos x 0 9559 tan x 0 3074 and

et u 1 2 1 and a 3 2 2 Find the vector component of u orthogonal to a Enter your answer symbolically wor in the formah

List the roots of the parabola y x 4x 29 In other words list the solutions of the equation 0 2 4x 29 Step 1 Identify the parameters A B and C A 1 B 4 C 29 Step 2 Compute the discriminant B 4AC the value of the discriminant is so we know that there will be no real solutions Step 3 Compute the other pieces of the quadratic formula What is B What is 24 Step 4 Finish computing the quadratic formula to get the root s B B 4AC 2A Note Your answers must be in exact form do not give their decimal values x B B2 4 2A

Problem 6 Find the area of the triangle with vertices 2 3 1 1 4 3 and 3 3 0 Enter your answer symbolically as in these examples 5 2

9 1 7 99x 119x 76x 96 11x 12 2 A 9x x 6 11x 12 3 11x 12 B 9x x 8 C 9x x 8 D 9x x 7 2 11x 12 9 21 154p 104 p 172p 2 14p 2 A 11p 9p 12 1 7p 4 5 B 11p 7p 10 C 11p 6p 8 D 11p 9p 11 2 14p 1 2 14p 1 2 14p 11 5x 24x 61x 30 5x 4 6 A x 4x 9 5x 4 8 B x 4x 9 C x 4x 9 D x 4x 7 5x 4 1 5x 4 5 5x 4 8 8 12 153y 48v 45 12 zoom 4 A v 12v 8 3 4v 3 2 B v 12v 4 3 4v 3 1 C v 12v 7 4v 3 D v 12v 5 10 12 10 224x 49x 90 14x 14x 7 A x 4x 14 8 14x 7 1 B x 4x 15 C x 4x 11 D x 4x 13 2x 1 4 14x 7 10 14x 7 12 16 92r 178r 116 8r 10 11 A 2r10r 12 8r 10 3 4r 5 7 B 2r 9r 11 C 2 10r 8 D 22 9r 13 8r 10 11 8r 10

1 9 9 21 154 p 104p 172p 2 14p 2 A 11p 9p 12 1 7p 5 B 11p 7p 10 C 1lp 6p 8 D 11p 9p 11 40 14p 2 14p C x 4x 9 1 D x 4x 7 11 5x 24x 61x 30 5x 4 6 A x 4x 9 5x 4 8 B x 4x 9 5x 4 1 2 14p 5x 4 5 5x 4 10 12 10 224x 49x 90 14x 14x 7 A x 4x 14 B x 4x 15 Cx 4x 11 1 D x 4x 13 8 14x 7 1 2x 1 4 14x 7 10 14x 7 12 16r 92r 178r 116 8r 10 A 2 10r 12 11 B 2 9r 11 C 2 10r 8 D 2r 9r 13 8r 10 3 4r 5 7 8r 10 11 8r 10

7 99x119x 76x 96 11x 12 8 8 12 153 48v 45 12 2 A 9x x 6 A 12v 8 2 11x 12 B 12v 4 B 9x x 8 3 C 9x x 8 D 9x x 7 11x 12 2 11x 12 4 9 21 154p 104 p2 172p 2 14p 2 A 11p 9p 12 1 7p 5 B 11p 7p 10 2 14p C 11p 6p 8 D 11p 9p 11 2 14p 1 2 14p 10 C 12v 7 D 12v 5 3 4v 3 2 3 4v 3 1 4v 3 10 224x 49x 90 14x 14x 1 A x 4x 14 7 8 14x 7 B x 4x 15 7 2x 1 4 14x 7 10 14x 7 C x 4x 11 D x 4x 13 ZOC

9 21 154p 104 p 172p 2 14p 2 A 11p 9p 12 1 7p 5 B 11p 7p 10 2 14p C 11p 6p 8 D 11p 9p 11 2 14p 1 2 14p 11 5x 24x2 61x 30 5x 4 A x 4x 9 B x 4x 9 C x 4x 9 D x 4x 7 6 5x 4 8 5x 4 1 5x 4 5 5x 4 12 10 10 224x 49x 90 14x 14x 7 A x 4x 14 B x 4x 15 C x 4x 11 D x 4x 13 4 8 14x 7 1 2x 1 4 14x 7 10 14x 7 12 16r 92r 178r 116 8r 10 11 A 2 10r 12 8r 10 3 B 2r 9r 11 2 C 2 10r 8 8r 10 D 2r 9r 13 11 4r 5 7 8r 10

7 99x 119x 76x 96 11x 12 2 A 9x x 6 11x 12 B 9x x 8 3 C 9x x 8 D 9x x 7 11x 12 2 11x 12 9 21 154p 104p 172p 2 14p 2 A 11p 9p 12 1 7p 5 B 11p 7p 10 C 11p 6p 8 D 11p 9p 11 2 14p 1 2 14p 1 2 14p 8 10 8 12 153 48v 45 12v 9 4 A 12v 8 3 4v 3 2 B 12v 4 3 4v 3 C v 12v 7 D v 12v 5 4 4v 3 10 224x 49x 90 14x 14x 7 8 A x 4x 14 14x 7 B x 4x 15 2x 1 4 C x 4x 11 D x 4x 13 14x 7 10 14x 7

4 Evaluate x 4 x 2 for x 5

3 Evaluate 3x 3 for x 2

4 Evaluate the expression 2 3x 20 10 for the value x 4

3 b 3b 32b 28 b 7 B b 46 1 C b 4b 4 D b 4b 4 1 b 7 5 n 4n 128n 143 n 13 A n 9n 11 B n 9n 8 C n 9n 10 D n 9n 8 1 n 13 3 n 13 n 13 C 4 4 6 4 K 13k 33k 30 k 10 1 k 10 A K 3k 4 B k 3k 3 C K 3K S D k 3k 6 k 10 6 k k 130k 24 k 12 A K 11k 2 B k 11k 5 k 12 C k 11k 4 5 k 12 D K 11k 4

1 3 W Divide 1 a 11a 13a 27 a 10 6 A a a 3 a 10 7 B a a 3 a 10 5 a 10 C a a 3 a 10 D a a 3 3 b 36 32b 28 b 7 2 b 7 A b 4b 3 B b 4b 1 C b 4b 4 D b 4b 4 4 b 7 5 n 4n 128n 143 n 13 AL O 11 c 4 6 2 2 x 14x 56x 59 x 8 A x 6x 9 6 9 1 8 B x 6x 9 C x 6x 6 D x 6x 8 A k 3k 4 B k 3k 3 C k 3k 5 4 k 13k 33k 30 k 10 1 k 10 8 x 8 x 8 5 x 8 D k 3k 6 5 k 10 6 k k 130k 24 k 12 A 22 116 2

1 3 Long Division Divide 1 a 11a 13a 27 a 10 6 A a a 3 a 10 7 B a a 3 C a a 5 a 10 a 10 Duket D a a 3 3 a 10 3 6 3b 32b 28 b 7 A b 4b 3 7 B b 4b 1 C b 4b 4 D b 4b 4 1 BROM 2 b 7 4 b 7 4 4 2 2 x 14x 56x 59 x 8 6 A x 6x 9 x 8 8 B x 6x 9 C x 6x 6 D x 6x 8 A K 3k 4 B k 3k 3 C k 3k 5 X 8 1 4 k 13k 33k 30 k 10 1 k 10 x 8 5 X 8 5 k 10 D k 3k 6

6 Simplify the following expression 1 2x 4y 6z 2 4x 3y 2

12 16r 92r 178r 116 8r 10 11 A 2r 10r 12 8r 10 3 B 2r 9r 11 4r 5 C 2r 10r 8 D 2r 9r 13 7 8r 10 11 8r 10

Long Division Divide 1 a 11a 13a 27 a 10 6 a 10 7 A a a 3 B a a 3 C a a a 10 5 a 10 D a a 3 3 a 10 3 b 3b 32b 28 b 7 A b 4b 3 B b 4b 1 C b 4b 4 D b 4b 4 2 b 7 4 b 7 5 n 4n 128n 143 n 13 A n 9n 11 1 n 13 3 B n 2 9n 8 C n 9n 10 D n 9n 8 n 13 1 n 13 4 2 6 2 x 14x 56x 59 x 8 6 A x 6x 9 x 8 8 B x 6x 9 C x 6x 6 D x 6x 8 A k 3k 4 B k 3k 3 C k 3k 5 x 8 1 4 k 13k 33k 30 k 10 1 k 10 D k 3k 6 x 8 5 x 8 5 k 10 6 k k 130k 24 k 12 A k 11k 2 B k 11k 5 k 12 5 k 12 C k 11k 4 D k 11k 4

Long Division Divide 1 a 11a 13a 27 a 10 6 A a a 3 a 10 7 B a a 3 C a a a 10 5 a 10 3 a 10 D a a 3 2 2 x 14x 56x 59 x 8 6 A x 6x 9 x 8 8 B x 6x 9 C x 6x 6 x 8 1 x 8 5 x 8 D x 6x 8

Long Division Divide 1 a 11a 13a 27 a 10 6 a 10 7 A a a 3 B a a 3 C a a a 10 5 a 10 D a a 3 3 a 10 3 b 3b 32b 28 b 7 A b 4b 3 B b 4b 1 C b 4b 4 D b 4b 4 2 b 7 4 b 7 5 n 4n 128n 143 n 13 A n 9n 11 1 n 13 3 B n 2 9n 8 C n 9n 10 D n 9n 8 n 13 1 n 13 4 2 6 2 x 14x 56x 59 x 8 6 A x 6x 9 x 8 8 B x 6x 9 C x 6x 6 D x 6x 8 A k 3k 4 B k 3k 3 C k 3k 5 x 8 1 4 k 13k 33k 30 k 10 1 k 10 D k 3k 6 x 8 5 x 8 5 k 10 6 k k 130k 24 k 12 A k 11k 2 B k 11k 5 k 12 5 k 12 C k 11k 4 D k 11k 4

7 99x 119x 76x 96 11x 12 8 8 12v 153v 48v 45 12v 9 4 A 9x x 6 3 4v 3 2 3 4v 3 1 4v 3 B 9x x 8 C 9x x 8 D 9x x 7 2 11x 12 3 11x 12 9 21 154p 104p 172p 2 14p 2 A 11p 9p 12 1 7p 5 B 11p 7p 10 C 11p 6p 8 2 11x 12 B x 4x 9 D 11p 9p 11 C x 4x 9 D x 4x 7 2 14p 1 2 14p 1 2 14p 11 5x 24x 61x A x 4x 9 30 5x 4 6 5x4 8 5x 4 1 5x 4 5 5x 4 10 12 A v 12v 8 B v 12v 4 C v 12v 7 D v 12v 5 10 224x49x 90 8 A x 4x 14 14x 7 1 B x 4x 15 C x 4x 11 D x 4x 13 2x 1 4 14x 7 10 14x 14x 7 B 2r 9r 11 12 16r 92r 178r 116 8r 10 11 A 2r 10r 12 C 2r 10r 8 D 2r 9r 13 14x 7 8r 10 3 4r 5 7 8r 10 11 8r 10

b 2 3x y 81y6x4 6

Find the rectangular coordinates for the point whose polar coordinates are given 3 5

36 The certificates of deposit pay 2 annually and the municipal bonds pay 4 annually Over a five year period the investor expects the blue chip stocks to return 10 annually and the growth stocks to return 14 annually The investor wants a combined annual return of 6 and also wants to have only one fourth of the portfolio invested in stocks

Angela owes 15 50 for text messaging in the month of July If her text messaging plan costs 11 for the first 600 messages and 30 for each additional text message how many text messages did she send that month Answer Keypad

K Give the degree measure of 0 if it exists Do not use a calculator 1 2 0 arccos Select the correct choice below and fill in any answer boxes in your choice 4 2 Type your answer in degrees O A OB 0 arccos arccos does not exist

Consider the inverse cosine function defined by y cos 1 x or y arccos x Complete parts a through d a What is its domain Points 0 of 1 Type your answer in interval notation Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers

Select the correct choice that completes the sentence below The point 1 lies on the graph of y tan x Therefore the point of 4 2 2 lies on the graph of y tan