Complex numbers Questions and Answers

Match each graph on the left with an interval where the function is constant 1 x 4 1 x 2 0 x 1 I I I I I

Solve the equation Check your solution 4x 6 2x 36

Evaluate the principal square root 25 169

mplity by factoring 175 175 Type an exact answer using radical

Tell if the radical is rational irrational or not a real number If the radical is rational find the exact value if the radical is irrationa write the approximate value rounded to two decimal places 144 s the radical rational irrational or not a real number O Not a real number Irrational O Rational Select the correct choice below and if necessary fill in the answer box to complete your choice A 144 Type an integer or a decimal Round to the nearest hundredth as needed

1 Determine whether is rational irrational or not a real number Evaluate the radical if it is rational If the ra 169 is irrational approximate the radical rounded to two decimal places Is 1 169 rational irrational or not a real number irrational Orational O A not a real number Select the correct choice below and if necessary fill in the answer box to complete your choice 1 169 Type an integer or a simplified fraction The radical is not a real number

implify by factoring 50 50 Type an exact answer using radicals

from Sines rule Sin A a T sin A Sin B Sinc Cos A 9448 In equation 1 6 9 2bc ak ab 79 ck b a b c 2x q b c 4x1 2 6 c 92 2x29bck Lbc Sinc c 9 b 2 ca bk ab sin c 9 b c 2 C 2 b 2 2 a c 9 b 9 46 c 2 abc k c 9 6 Cos B 209 9 8 c dab ck 55 2 1 ab sinc 4 9 b c 246

a i Describe the set of points in the complex plane that satisfy the inequality 2 z 9 4i 3 ii Provide a hand sketch of this region iii Find the area of this region b Describe the set of points in the complex plane that satisfy z z 4

Explore 6 1 6 2 Create a hanger using all of these shapes 5 circles 4 triangles 3 squares 5X Determine the value of x that will balance it x 344 A4

Problem 1 Enter the following 3 matrices into Matlab Problem 1 a Problem 1 b 27 28 48 38 47 18 44 7 A 14 35 30 14 32 13 44 33 17 23 17 2 B ATCB 26 1 18 25 41 46 30 C 2 1 6 14 2 6 44 5 44 38 To check that you have correctly entered these matrices into Matlab verify that 62675 3337 44933 109842 42703 24803 68129 49438 24542 11410 34418 31620 33815 2227 24953 58782 and that tr ACB 13508 a Let D CBAT Find d42 i e find the entry in row 4 column 2 of the matrix D b Let E ABTCT Find tr E c Let F be the reduced row echelon form of AFCB Find f 4 i e find the entry in row 1 column 4 of the reduced row echelon form of ATCB

e Page 67 4 2 Determine whether something is living or nonliving based on the charac Which of the following are living scientists such as Daniel Gibson a rocky outcropping a petri dish bacteria like Mycoplasma mycoides nonliving living tics

Graph the following elements on a number line then determine the maximum minimum and mean of these data 2 7 6 Graph 2 10 8 3 BOOK 0

Instructions Find the missing probability P B P A B 9 20 P A and B 50 X 100

Instructions Find the missing probability P B P A and B 3 25 P A B

Make m the subject Nw tm I 1 r

exact values below If applicable click on Undef 225 22 8 X Une

For the following right triangle find the side length x X 6 8 0

12 x L Arrastre para mostrar el ngulo X

y e x 28 23 37 a Solve out for the values of y x 0 and a a b What would the angle created between the hypotenuse of 28 and line 23 be c What would the angle created between the hypotenuse of 37 and line y be

5 5 f x x 4x 1 Find 1 A 7 C 1 B 1 D 4 7 f x x 2x 1 Find 1 6 8 6 1x 3x 4 4 Find 0 A 1 0 B 8 D 3 8 tx x 4 1 Find 10

9 7 f x x 2x 1 Find 1 9 x x 4x 3 Find 2 8 10 8 f x x 4 1 Find 10 10 x 3 x 4 2 Find 6

Solve and check the linear equation 10 X N 2 11 x3 X

An integer a 40 it said to be divide integer b if there exists an integer k such that b ak it le denoted by a b Ex 02 8 8 2 4 3 24 24 3 8 It a does not divides b denoted by a b It a b a 6 3 It a b a b Properties of dinsibility It a b then P T a bx where x ie an integer Pt Guven a b b ak kez Note x B Sx bx ak x k x K 2

Consider the following f x 2x 7 a Write the formula for f x dx b Write the formula for 2 16x dx f x dx f x dx Use C for the constant of integration X 10x dx f x dx

A car is driving away from a crosswalk The formula d t 2t expresses the car s distance from the crosswalk in feet d in terms of number of seconds t since the car started moving a Suppose t varies from t 2 tot 5 i Does the car travel at a constant speed over this interval of time No ii What is the car s average speed over this interval of time feet per second Preview b Suppose t varies from t 1 7 to t 2 5 i Does the car travel at a constant speed over this interval of time No ii What is the car s average speed over this interval of time feet per second Preview

Problem 1 Find the exact values of the other five trigonometric functions of t by using information 7 25 a cos t b tan t c csc t 1 7 2 5 2 such that the terminal s Quadrant II such that sec t 0 such that cot t 0

5 Shown on the right is the graph of y X Determine its symmetries if any This graph is O A symmetric to the origin B symmetric to the x axis OC symmetric to the y axis D not symmetric to the x axis y axis or origin C P 49 B B q

Determine whether the function is even odd or neither Then determine whether the function s graph is symmetric with respect to the y axis the origin or neither 6 g x x 4x Determine whether the function is even odd or neither Choose the correct answer below even odd neither

a Given that 1 where n Z n 1 Find the roots of the equations for the various values of n and complete the table below 77 3 4 5 6 7 750 51 1 Roots 73 Sum of the roots What conclusion can you make b Find the roots of the equation 1 0 where n 2 Represent these roots on the Argand 2 7 diagram Suppose w e is the root with the smallest positive argument express the other roots in terms of w Show that 1 w w w w 0 using i the sum of geometric series the expansion of z 1 1 z 2 2 c For any two complex numbers and w use the properties of a complex conjugate to establish the relationship wf z wf 2 P wf Sketch and was vectors on an Argand plane If the vectors and w form a parallelogram find the length of the diagonals of the parallelogram in terms of and w Give a geometric interpretation of

ky my2 dx Now we will try to decompose the coefficient of into partial fractions dy dx 1 A B Let y k my yk my where A and B are constants to be determined From 6 we get 1 A k my By which gives 1 Ak and 1 or A Hence and B 1 y k my ky Bk m m 1 k k my Thus the given differential equation can be rewritten as 1 1 m dy 1 ky kk my or For the case under consideration Eqn 7 can be expressed as ny In k my 1 for y0 and k my 0 In the integration of Eqn 7 the signs of y and k my play an important role We now discuss the following possible cases Case 1 y 0 and k my 0 0 y k which on integrating yields 6 7 Iny In k my x C where e is a constant of integration The above equation can be further express as In y In k my x c 1 4 my exp x c Case II y 0 When y 0 then k my 0 because m 0 k 0 In this case Eqn 7 on integration can be written as

For each of the series below select the letter from A to C that best applies and the letter from D to K that best applies A possible answer is AF for example A The series is absolutely convergent B The series converges but not absolutely C The series diverges D The alternating series test shows the series converges E The series is a p series or a constant multiple of a p series F The series is a geometric series G We can decide whether this series converges by comparison with a p series but the series is not a p series or a constant multiple of one H We can decide whether this series converges by comparison with a geometric series I Partial sums of the series telescope J The terms of the series do not have limit zero K We can decide using the integral test NOTE Make sure that you can provide the proper arguments to support your answers 818181818 1 4n ln n cos nn NT 2n 5 n n n 6 sin n n cos n Activa Go to S

3 5 points each Find the Area and Perimeter of the following sector A P 128 12 ft radius

Complete the following sentence To clear the decimals in the equation 0 84x 9 4 0 2x multiply both sides of the equation by o clear the decimals in the equation 0 84x 9 4 0 2x multiply both sides of the equation by Type a whole number

Solve the equation Check your answer 1 5 6 1 x 3

olve the equation Check your solution 4 3y 3 9 6 y 6 3y

Solve the equation by multiplying by the least common denominator LCD 7 15 13 6 x 3 13 30 fraction

Solve the equation c 0 95c 8

Solve the equation 2x 5X 5 Step by Step Solution it without fractions Do this by multiplying both sides of the ec

Solve the equation Check your solution 2 5n 8 22 lified fractio

2 If Jenna s earnings w after working h hours can be represented by the equation w 12h how many more hours would she need to work in a week if she wants to earn an additional 60 per week

6 Given the equation y kx what is the value of k if y 12 and x 4

4 Given the equation y kx what is the value of x if y 10 and k 5

Solve the equation Check your solution 15 3a 6a 2

Solve the equation Check your solution 9 4 9 y

Solve the equation Check your solution 4 x 4 5 15

Solve the equation Check your solution 5x8 4x 44

Solve the equation Check your solution 9 3z 27

Solve the equation Check your solution 3p 3 21

10 y x 45 4 3 2 F 1 3 5 11 y x y IX 10 45433 S 12 2y 3x r 44 5