Complex numbers Questions and Answers

Examine the following graph of a function modeling damped harmonic motion. Find the equation for the function pictured in terms of y and t. Assume that a factor of e-te-t provides the desired damping effect and that the graph has no vertical or horizontal shifts.

Decide if the following is rational or irrational: √64

Add or subtract as indicated and write the result in standard form. (5 - 6i) + (9 +91) 14-3i -14-3i 14 + 3i -4 + 15i

Find the product and write the result in standard form. (-6 +9i)(5 + i) -21 +39i -21-51i -39 + 39i -39 - 51

Suppose a is a non-zero algebric number and 3 is a transcendental number. Show that a +3 and aß are transcendental numbers.

Divide and express the result in standard form. 4+5i / 5-4i -1 1 i -i

Multiply. [x-(6-2i)][x-(6+2i)] Note that these expressions contain complex numbers. Simplify your answer as much as possible.

Find all zeros of f(x) = x³ + 4x² + x + 4. Enter the zeros separated by commas, using exact values, not decimal approximations.

Let z be a complex number, and let n be a positive integer such that z" = (z + 1)" = 1. a) Prove that |z| = |z + 1| = 1. b) Find the possible values of z in exponential form. c) Prove that n must be divisible by 6.

Let Po, P₁, and p₂ be the orthogonal polynomials described below, where the inner product on P4, is given by evaluation at -2, -1,0, 1, and 2. Find the orthogonal projection of 3t^3 onto Span (Po.P₁ P₂). Po(t) = 4 P₁ (t) = 2t P₂ (t) = t^2-2

Solve the inequality: -25> x - 27 Enter your answer as an interval, such as [a, ∞).

For each subfield S of Q[i, z], determine Auts (Q[i, z]).

Use the given transformation to evaluate the integral. where R is the triangular region with vertices (0, 0), (7, 1), and (1, 7). x = 7u + v, y = u +7v

If z = x + iy and z+3/z-3 lies on the y-axis of complex plane, where z ≠3, then which of the following options is correct? (a) y = 0 (b) x² + y² = 4 (c) x² + y² = 94 (d) x = 0

A 100 acre plot of land has a concentration time of 80 minutes. The area is residential single family homes with a C-0.40. What is the percent increase in stormwater runoff from a 50 year recurrence event versus a 25 year event? Use the Rational Equation to solve this problem. Select the best answer as reading Figure 4.2 may give you a slightly different answer than the correct answer provided below. 25.3% 14.3% 32.0% 82 %

Find the angle θ between v=cos 7π/4i+sin7π/4j and z= cos4π/3i+sin 4π/3j.

Evaluate T/3 using a double angle indetity

Evaluate π/3 using a double angle indetity

Find all solutions to 2 cos (0) = -1 on the interval 0 ≤ 0 < 2m. Solve 7 sin(26) +5 sin(o)= 0 for all solutions 0 < < 2. Ø Give your answers accurate to at least 2 decimal places and in a list separated by con

ABCD is a parallelogram with coordinates A(4, 2), B(3,-1), C(-1,-1), and D(-1, 2). To prove that ABCD is a rhombus, you would plot the parallelogram on a coordinate plane and then find which of the following? (A) measures of the angles (B) lengths of the diagonals (C) slopes of the diagonals (D) midpoints of the diagonals

Verify the identity: cos (2A)/ 1 + sin (24)= cot A-1/cot A + 1

The population in a certain city was 58,000 in 2000, and its future size is predicted to be P(t) = 58,000 e 0.014t, where t is the number of years after 2000. Complete parts a through d below. a. Does this model indicate that the population is increasing or decreasing? b. Use this function to estimate the population of the city in 2003.

What is the linen valuation of bath towels in a property that has 2,500 pieces in stock purchased at $14.95 each and 288 just bought at $16.50 each? a $43,92350 b $39,423.50 C $32,419.50 d $23,394.50 e $23,439.50

Find all the zeros of the polynomial f(x)=x²-x²+2x² - 4x-8 given that -2i is a root.

1. Cooking temperature for chicken should be between 165 and 175 degrees F. Inequality; 165 ≤x≤ 175 Interval notation; [165 F,175 F] 2. The number of shipments should not exceed 10. Inequality; x < 10 Interval notation; [0,9] 3. city should have more than 5 restaurants. Inequality; x>5 Interval notation; [6,infinity] 4. The number of new COVID-19 infections should be less than 2, and recoveries should be more than 5. Inequality; x<2, x>5 Interval notation; [0,1],[6,infinity]

Which of the following statements is FALSE? f(z)=z + 1/z+1 is a fractional linear transformation f(z) = z² is a conformal map from the right half-plane {z : Re(z)>0} onto its image If f is a fractional linear transformation with f(x) = ∞, then f must be affine The image of a circle in the plane under a conformal map is not necessarily a circle

Let a, b, c be complex numbers satisfying b-a /c - a=a-c/b-c Considering the triangle with vertices a, b, c. Prove |b-a| = |c-a| = |b-c|.

The half-life of radium-226 is 1600 years. Suppose you have a 20-mg sample. How long will it take to decay to 7-mg? Round to 4 decimal places.

Find all the complex fourth roots in rectangular form of w = 81 ( cos 4π/3 + i sin 4π/3 ) z0 z1 z2 z3

ln (3, 5) secret sharing scheme, the dealer selects K=15, h(x)=5x^2+6x+15 mod 19. show how three shadow holders x-=1,3 and 5 can construct the master secret K

Consider the set of real numbers and the set of complex numbers. Is every real number also a complex number? Is every complex number also a real number? Explain.

If cos θ = 3/4 and θ terminates in Quadrant IV, find the exact value of each of the following. Caution: The triangle is not a 3-4-5 since the hypotenuse given is 4.

If function h has an inverse and h-¹(1) = -4, find h(-4). h(-4)=

A Chevrolet Sonic Hatchback costs $14,785.00. With a 11% down payment, you can have an amortized loan for 8 years at a rate of 4.5%. What will the monthly payment be? How much will the car cost, in total? How much money will be paid in interest?

State the intervals of the domain where the given function is increasing or decreasing. You may want to create a graph of the function, using your knowledge of transformations, in order to answer this question. f(x)=|x+3|-4

One of your tenants has ten years remaining on a lease at $3,500 per month. The space is now worth $4,000 per month. An adjacent tenant wants to expand their space, so you want to make arrangements to buy out the first tenant's lease in order to lease it to the expanding tenant at fur market value. The market discount rate is 10%. What is the maximum you would be willing to pay to buy out the lease? Select one a. $4.999.85 b $25.43578 c$37,835.58 d $60,000.00

For the function given below, set up and then completely simplify the expression for f(x+h)-f(x) f(x)=7x² - 4x For partial credit, enter the first step, just the meaning of the calculation in its unsimplified form: Now enter the final answer, in its completely simplified form. If the original form above cannot be simplified, type "CBS".

Use the "Five-Point Method" for graphing one period of the following function: y = -3 sin[2(x - π)]

A rental car company charges $35 plus 40 cents per each mile driven. Part1. Which of the following could be used to model the total cost of the rental where m represents the miles driven. C = 0.4m + 35 C = 4m + 35 C = 40m + 35 Part 2. The total cost of driving 400 miles is

A soap manufacturing company was distributing a particular brand of soap through a large number of retail shops. Before a heavy advertisement campaign, the mean sales per week was 140 dozens. After the campaign, a sample of 26 shops was taken and the mean was found to be 147 dozens with standard deviation 16. Can you consider the advertisement effective?

A movie theater has a seating capacity of 203. The theater charges $5.00 for children, $7.00 for students, and $12.00 for adults. There are half as many adults as there are children. If the total ticket sales was $ 1458, How many children, students, and adults attended?

What was transferred from the hydrochloric acid to the water molecule? Click on the background to slide down the LabPad and have a look again. a) A hydrogen atom b) An electron c) H+ d) A water molecule

In Electrical Engineering, complex numbers are used to describe current, voltage, and impedance in a circuit, and these three quantities are related by the equation E = IZ. Find Z if E = 2 + 3i and I = 2 + i. Simplify your answer and write it in a + bi form.

The accessories buyer sold a group of pearl earrings very well. 1150 pairs were sold at $10.00 each. To clear the remaining stock the buyer reduced the remaining 50 pairs on hand to one half price. What was the percent of markdown sales to total sales?

For f(x) = x + 2 and g(x) = 5x + 5, find the following functions. a. (fog)(x); b. (gof)(x); c. (fog)(0); d. (gof)(0) a. (fog)(x) = (Simplify your answer.)

Determine whether the set W is a subspace of R³ with the standard operations. Justify your answer W = {(a,a-3b,b): a and b are real numbers}

Find the inverse of the function. y = 8x 6 Select one: a. 3x/4 b. 4x/3 c. x+6/8 d. X-6/8

A real estate license holder may do all of the following EXCEPT A) explain business details. B) explain the general content. C) explain factual statements. D) give legal advice.

When a legally enforceable promise is exchanged for a legally enforceable promise, A) an offer is made. B) a contract is created. C) an executed note is made. D) an acceptance and counteroffer is made.

How many back-up contracts can be created using the TREC-promulgated addendum for that purpose? A) As many as the seller wants B) No more than two C) One D) Equipment