### Complex Eigenvalues

Find the solution to the given system for the given initial condition x'(t)= [1,0,-1;0,2,0;1,0,1]x(t) for a.) x(0)= [-2;2;-1] b.) x(-pi)=[0;1;1]

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Find the solution to the given system for the given initial condition x'(t)= [1,0,-1;0,2,0;1,0,1]x(t) for a.) x(0)= [-2;2;-1] b.) x(-pi)=[0;1;1]

Let G be an open subset of C ( complex plane) and let P be a polygon in G from a to b. Use the following 2 theorems to show that there is a polygon Q in G from a to b which is composed of line segments which are parallel to either the real or imaginary axes. The 2 theorems are: 1). Theorem: Suppose f: X --> omega is continuou

Show that transformation W (Z) = (a Z + b) / (c Z + d) of the upper half of a complex plane is 1-1 and onto the upper half plane if a, b, c, and d are real and satisfy condition a d > b c

To find theta, and prove that {e^{in theta} : n nonnegative integer} is a dense subset of the unit circle.

Show that { cis k : k is a non-negative ineger} is dense in T = { z in C ( C here is complex plane) : |z| = 1 }. For which values of theta is { cis ( k*theta) : K is a non-negative integer} dense in T ? P. S. cis k = cos k + i sin k, i here is square root of -1. I want a full justification for each step or claim.

Let V be a circle lying in S. Then there is a unique plane P in R^3 such that p / S = V ( / = intersection). Recall from analytuc geomerty that P = { (x_1,x_2,x_3) : x_1 b_1 + x_2 b_2 + x_3 b_3 = L, where L is a real number}. Where ( b_1,b_2,b_3) is a vector orthogonal to P . It can be assumed that (b_1)^2 + (b_2)^2 + (b_3)

What is the solution (-1+i squareroot of 3)exponent 9?

Given f(z), determine f'(z), where it exists and state where f is analytic and where it is not: x + i sin y

Obtain, in polar form all values z^(2/3), z^(3/2) and z^pi for each given z. Obtain, in Cartesian form all values z^i, z^(1-i) 2 + 2i

With a labeled sketch, show the point sets defined by the following: |z|<|z-4| 2≤|z+i|≤5

Evaluate |(2-i)^3 / (1+3i)^2|

(See attached file for full problem description) --- - flow around a corner... - components of velocity... --- (See attached file for full problem description)

See the attachment for the problems. --- - the image of the closed rectangular region... - principal branch of the square root... --- (See attached file for full problem description)

A payoff table is given as ..... a. What choice should be made by the optimistic decision maker? b. What choice should be made by the conservative decision maker? c. What decision should be made under minimax regret? d. If the probabilities of E, F, and G are .2, .5, and .3, respectively, then e. What choice should be ma

Please see the attached file.

See the attachment (77-7) for the problem. and you should also see the examples in section 77 in order to solve it. I also attached section 77 (example1-1 and example1-2).

4. (Separation) Seeking a solution u(x, t) = X(x)T(t) for the given PDE, carry out steps analogous to equations (3)?(6), and derive ODE's analogous to (7a,b). Take the separation constant to be ?K2, as we do in (6). Obtain general solutions of those ODE's (distinguishing any special ic values, as necessary) and use superposition

Use three-digit rounding arithmetic to compute the following sums (sum in the given order): (See attachment for full question)

The double angle formulae are easy to learn: Sin 2x = 2 sin x cos x Cos 2x = (cos x)^2 - (sin x)^2 but working out Cos 4x say in terms of cos x and sin x by using identities such as Cos(A + B) = Cos A Cos B - Sin A Sin B is laborious. Find a simple method to work out any multiple angle formula, using De Moivre'

Write the expression i^6-5 in the standard form a + bi

A. A certain fluid is flowing with a constant speed V in a direction making an angle B with the positive x-axis. Find the complex potential for the fluid under consideration. Also determine the velocity and the stream functions.

Complex Variables Existence of a Function Show that the derivative of the following function does not exists at any point

Given that cos x=(e^jx + e^-jx)/2 and sin x=(e^jx - e^-jx)/2j Using ONLY this information, prove that: cosAsinB=1/2[sin(A+B)- sin(A-B)]

Using the following data, obtained from an imaginary harness small manufacturing company, determine the correlation between the number of hours that an employee works and how many belts they produce: Hours Worked 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 Belts Produced 2 3 3 4 5 6 6

What is the complex conjugate of 78.93iw^3+30.48iw^2+iw? How did you find it?

1) For each weighted voting system , find all dictators (d), veto power players( vp), and dummies (d) ( 7: 7,3,2,1) 2) For the weighted voting system ( 12: 6,4,3,1,1,) a) Find what percent of the total vote is the quota. b) In a Shapley-Shubik distribution system , how many sequential coalitions would be formed from thi

Find a conformal mapping from the unit disc Δ(0,1) = {z|z|<1} to D={z:|z|<1}[0,1]. Please see attached for diagram.

Use Cauchy's formula for the derivative to prove that if f is entire and |f(z)|≤ A|z|² + B|z| + C for all zεC, then f(z) = az² +bz + c Please see attached for full question.

Simplify the following (3+i )/2 + (1- i )/4

Use the formal method, involving an infinite series of residues and illustrated in the examples. 7. F(s) = 1/(s cosh (s^½)) Please see attachment for full question.