### Complex numbers

1. Find all the values of z in the form a+bi such that (a),(b),(c) (please see the attachment) 2. Find the real part u(x,y) and determine if it is harmonic. (please see the attachment)

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1. Find all the values of z in the form a+bi such that (a),(b),(c) (please see the attachment) 2. Find the real part u(x,y) and determine if it is harmonic. (please see the attachment)

Let f be analytic inside and on the unit circle. Suppose that 0<|f(z)|<1 if |z| = 1. Show that f has exactly one fixed point inside the unit circle. ( note : a fixed point is a point Zo such that f(Zo) = Zo).

I have attached chapter 1 description pages. I need following problems. Page 16 : - Problem Number: - 10 Page 17: - Problem Number: - 15 Page 19: - Problem Numbers :- 5 and 8 Please mention each and every step. Thanking you

Can you show me how to work this? Is there only one way and what is most acceptable? Find the values of the complex conjugate roots for the equation x^3 + 3X^2 +2 = 0.

Find to three decimal places the one real root of X^3 + 3X^2 + 2 = 0. Then use the approximate real root and compute the two conjugate roots using the graphical method of Yanosik.

Mathematicians say that division by zero is forbidden. The expression 5/0, for example, is undefined. "Undefined" in this sense means "unable to be determined". Why is this? When we divide 5 by 5 (5/5) we get 1. Divide 5 by 2 we get 2.5. Each time we make the denominator smaller in the expression 5/x, the expression gets

Please see the attached file for the fully formatted problems.

Determine if the following equations are real or complex; explain the answer in detail. Determine whether the following equations real or complex solutions; justify your answer. Note: It is not necessary to find the solutions; just determine if they are real or complex and explain why. a) 5x2 + 8x + 7 = 0 b) (7)1/2y2 - 6

Suppose that V is a complex (i.e. F = C) inner-product space. Prove that if N, an element of L(V), is normal and nilpotent, then N = 0. Use Complex Spectral Theorem: Suppose that V is a complex inner-product space and T is an element of L(v). Then V has an orthonormal basis consisting of eigenvectors of T if and only if T

Perform the indicated operations. Write the answer in the form a + bi. 2+4i (9+4i)

How many times does the graph of a quadratic equation (a parabola) cross the x-axis? I know that the graph of a quadratic equation should cross the x-axis 2 times, because the polynomial equation of second degree should have two roots, however if the vertex of a parabola is the orgin itself, the two points are coincident,

Determine if the following have a solution or not? justify answer. (apply the discriminant) are the roots real, repeated real, or complex? 1) 5x^2+8x+7=0 2) (7)^1/2y^2-6y-13(7)^1/2=0 3) 2x^2=x-1=0 4) 4/3x^2-2x+3/4=0 5) 2x^2+5x+5=0 6) p^2-4p+4=0 7) m^2=m+1=0 8) 3z^2+z-1=0

Determine if the following equations have a solution or not? justify your answer. are the roots real, repeated real or complex? Q:) if x=3 and x= -5, then form a quadratic equation.

Please see attached file for full problem description. 1. B = 54 degrees, C = 112, and b = 18 2. Solve the equation on the interval [0, 2pi]: (cosx)^2 + 2 cos x + 1 = 0 3. Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. C = 110°, a = 5, b = 11 4. Solve the triangle.

I need to find all real or imaginary solutions to this equation. Please see attached

Briefly explain why the use of integer variables creates additional restrictions but provides additional flexibility.

Given the complex numbers z1 = 5 - j4 z2 = 4 + j z3 = -6 - j7 z4 = j2 Calculate, giving your answers in the form a + jb, the following:- (i) z4 - z1 + z2 (ii) 3z1 - 2z3 + z4 (iii) z1z2 (iv) z3/z2

In the following equation by equating real and imaginary parts, find expressions for R6 and L in terms of R1, R2, R3, R4, R5 and C, given that the frequency is one radian per second. See attached file for full problem description.

I have some Quantitative Analysis questions I need help understanding. Waiting lines and queuing Theory models 1. The New Providence shopping mall is considering setting up an information desk manned by one employee. Because of the complex design of the mall, it is expected that people will arrive at the desk at about twi

(1) Let G = {z : 0 < abs(z) < R} for some R > 0 and let f be analytic on the punctured disk G with Laurent Series f(z) = sum a_n*z^n (from n = -oo to oo). (a) If f_n(z) = sum a_k*z^k (from k =-oo to n), then prove that f_n converges pointwise f in C(G,C) (all continuous functions from G to C (complex)); i.e., {f_n}

If is analytic in a domain containing the x-axis and the upper half-plane and in this domain, then the values of the harmonic function in the upper half-plane are given in terms of its values on the x-axis by (y>0). Below is an outline for the derivation, I just need to figure out how to justify the steps.

Mr. Davison has been operating a small bicycle shop at the same location near Aspen, Colorado for 50 years. What type of decisions must he make in operating his business? On what basis would he likely be making these decisions? How do you think Mr. Davison would respond to a suggestion that he hire a quantitative analyst to assi

x ------------------ = 0.007 754 1 + i --------- y 42425 x -------------------------------------- = 1 754 (1+ i -------) *500* (1 + i 41.47) y USING THESE TWO EQUATIONS SOLVE FOR X=? AND Y=?

Prove that if T is a Mobius transformation such that T(0) = 0, then T may be written as T(z) = z/(cz+d) for some choices of c and d.

Write each expression in the form of a+bi, where a and b are are real numbers 1. -3i/3-6i 2. -2-sqrt-27/-6

If the solution to an equation is imaginary or irrational, it takes a bit more effort to check. Replace x by each given number to verify the following statement. Both 2+3i and 2-3i satisfy x^2 -4x+13=0

Y < -2 + 7 i need help to solve this equation and the steps on how to solve it.

Using the gcd for 85 and 1+13i, by the Euclidean Algorithm.

Use Demoivre's theorem to write [3 cis(pi/2)]squared in the form a+bi without trigonometric functions. Find the real and complex solution of the equation Xsquared - 8 = 0 Find the angle between the two vectors (5,2) and (-2,5)

Let f(z) be analytic in a region G and set φ(z,w) = (f(w)-f(z))/(w-z) for w,z Є G w ≠ z. Let z0 Є G. Show that lim (z,w)-->(z0,z0) φ(z,w) =f'(z0). Complex Variables. See attached file for full problem description