Given the complex numbers find the real and imaginary parts of the complex number: Re ( 2 ) = Im (2) = = Also find writing your answer in the form a +i. b. - 1 Leave your answers as fractions. + i* z=-1+5 i w=3+9i

Q: 1. For each solution. congruence determine whether there is a J X² = -1 (mod 397) (397 is prime) CC…

A: We shall be using the result regarding the value of legendre symbol

Q: Create an equation and sketch the graph of a function using the following table: Time 0 15 30 45 60…

A: We need to sketch the the graph and calculate the equation of a function using the given table.

Q: f(x) = cos r 22 g(x) f* 0 2' når x = 0 når x = 0. = = f(t) dt, der ƒ er som i (a). f

A: The given functions are (a)  and (b) .We need to find Maclaurin series and interval of convergence.

Q: As discussed in the Mythical Man Month, consider the situation shown below where the time to…

A: Number of workers is :The time taken by 3 workers is :The main aim is to find the number of…

Q: Which of the following solves the initial value problem x²y" 5xy' +9y = 0, y (1)= 1, y'(1) = 0.

A:

Q: 4. The transformation equations from the x-y to u-v co-ordinate systems are given by 1 u = x+y y x +…

A: The objective of the question is to find the region in the u-v coordinate system that corresponds to…

Q: 28. Show that tan z = sin(2x) + i sinh(2y) cos(2x) + cosh (2y)

A: We can show the given identity.

Q: Prove:

A: The proof of the statement is given in the explanation part.Explanation:Steps and explanations are…

Q: the following equation cally in three different g 9 +119 = 69=0

A:

Q: In a harbour, there are 2 landing places. Ships arrive at a rate of 8 per day (exponentially…

A: a. Average queue length for the current system: To find the average queue length, we can use the…

Q: Ux + Uy u

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: Consider a random graph G(N, p) with eln 2 3N p= = In the limit N → ∞ the average degree (k) is…

A: The objective of the question is to determine the average degree (k) of a random graph G(N, p) in…

Q: Find the inverse of the function, s(t) = √3 – t² − 6

A:

Q: 2 - du dx du +3 = 0 dy Solution of Partial Differential equation By Separation of Variable Method

A: (.) Given partial differential equation is,            (.) In method of separation of variables we…

Q: I need help with this complex variable question

A: 2.{zn​} converges to z if and only if ∣zn​−z∣ converges to 0Explanation:

Q: The graphs of y=b(x)(black), y=g(x)(green), y=p(x) (blue) and y=r(x) (red) are shown. Which of the…

A:

Q: Hi I need help with 2a) and b)

A: Below there is clear explanation Explanation:2) a). Maclaurin series expansion for y(z)=4z+1/​3z2…

Q: It is possible to hire apprentice workers who will need to be trained. For training, up to three…

A: To formulate linear programming equation which will maximize profit over the four…

Q: Consider the sequences made of the letters a, b, c, d, e. let yn be the number of such sequences of…

A: Consider the sequences made of the letters .Let  be the number of such sequences of length  in which…

Q: #4: Consider the equation ex+ 5y + 3x + 25y + sin(xyz) + 15:= 1 The implicit function theorem…

A: We will find the partial differential of the equation.

Q: Given the following graph of the function y = f(x) and n = 6, answer the following questions about…

A: Given the function y=f(x) and n=6.From the graph, we note the following:xnf(xn)0516283645.55567

Q: Line 1 is defined by slope m = -2 and y-intercept c = 4 . Line 2 passes through the points (x, y)…

A: See the Explanation section Explanation:(a) Line 1: m=-2; c=4Slope-intercept form: y=mx+c Line 1:…

Q: Solve the following systems of linear equations using Gauss-Jordan Elimination method.  0.25x –…

A:

Q: Good Day Kindly help me to classify the following series.

A: a) This is an arithmetic progression sequence.b) This is an alternating series.Explanation:Step 1:…

Q: Find the following Eigenvalues and corresponding Eige vectors. Verify that the Eigenvectors are…

A: The objective of this question is to find the eigenvalues and corresponding eigenvectors of the…

Q: B₂ = {(2₂1 X12 X22 |xij≥0 for i, j = 1, 2, X11 + 12 = 2, X21 + x22 = 2, x11 + x21 = 1.5, x12 + x22 =…

A: Since you have posted a question with multiple subparts, we will solve the first three subparts…

Q: (2) (a) Use an element proof to prove that for any sets A, B, and C, if A C C and BCC, then AUBCC.…

A: a. Assume that x∈A∪B. This means that x is either in A or in B or possibly in both.Since A⊆C, if…

Q: Find a particular solution y of the following equation using the Method of Undetermined…

A:

Q: Given a = [2, 1, 01, b = [-3, 2, 01, c = [1, 4, -2] and d = [5, -1, 31, find: For a = [cos t, sin t,…

A:

Q: Suppose f (x, y) = , P = (-2, -1) and v = 2i - 4j. A. Find the gradient of f. (Vƒ)(x, y) =i+j Note:…

A: Since you have posted a question with sub-parts greater than three. We will provide the solution…

Q: 4. y = sin 2x 1-cos 2x

A: We have to find the derivative of

Q: Calculate the volume of the bottle using triple integrals (THOUGH IT IS APPROXIMATE, BUT CALCULATE…

A: To calculate the volume of the bottle using triple integrals, we can break the bottle into three…

Q: Theorem 4.27 says that if f [a, b] → R is Riemann integrable then f² [a, b] → : 3 R is Riemann…

A:

Q: An investment of $10,000 earns interest at an annual rate of 6.7% compounded continuously. Find the…

A: Let's find the instantaneous rate of change in the amount in the account when it reaches We can use…

Q: Using 10 vertices, create a weighted connected graph with the following characteristics: The…

A: The objective of this question is to create a weighted connected graph with 10 vertices, labeled…

Q: Verify that there exists a function g: R² → R² such that ū = (u, v) = g(x) for the system 4x² + 5yv4…

A: Given the system .Rewriting as, .We can apply the inverse function theorem that says for a…

Q: A credit card company offers an annual 2% cash-back rebate on all gasoline purchases. If a family…

A: Given:A credit card company offers an annual 2% cash-back rebate on all gasoline purchases. If a…

Q: Find the following Eigenvalues and corresponding Eige vectors. Verify that the Eigenvectors are…

A: Since you have posted multiple matrix with single question. We will provide the solution only to the…

Q: Using the example, can you show the Laurent series for (2+3z)/(z^2+z^z^4), 0<abs(z)<1

A: The answer will be,…

Q: Identify each of the following matrices as either symmetric, skew-symmetric, or orthogonal. Prove…

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Q: 8. Carrot the Cat Carrot the cat likes taking naps in one of four locations: the rug, the bed, the…

A: Carrot has the following conditions:• He will not sleep in the sink twice in a row• He will sleep on…

Q: Disprove the following statement by giving a counterexample. For every integer p, if p is prime then…

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Q: Determine the derivatives of the following functions.. 1. y = 6 cos 4x 2. y = 3 sec 2x 3. y=tan(25x)…

A: Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: 1 2 I - du dx du - dx = du dy +3 du 一 dy Solution of Partial Differential equation By Separation of…

A: Note: ''As per guidelines we will solve the first question. If you want any specific question to be…

Q: Please help me with these questions. I

A: The objective of the question is to determine whether the set of rational numbers is countable and…

Q: Use the variation of parameters to solve the given equation: (a) y" +4y=2cot 2x

A: Note that : Since you have posted multiple questions, we will provide the solution only to the first…

Q: Use interval notation to write the intervals over which fis (a) increasing, (b) decreasing, and (c)…

A: Given, a graph of the function .It is required to write the interval for which the following…

Q: Kim's Sausage House is preparing for Restaurant Week. Many upscale Italian restaurants in NYC have…

A: Kim's Sausage House is preparing for Restaurant Week. Many upscale Italian restaurants in NYC have…

Q: Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200…

A: (a) The initial value problem for this scenario involves a differential equation representing the…

Q: A town want to replace an existing bridge that cost $5000 annually in an operation and maintenance…

A: Certainly! Let's calculate the single payment present worth of the existing bridge's operation and…