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Complex Analysis

Solving Complex Equations

I need to solve for all of the roots of (z+1)^4 = (1-i). Any idea on how to do it? keywords: imaginary

Verifying a Complex Root

Verify the z = (3-2j) is a root of the polynomial 2z^4 - 18z^3 +66z^2 - 102z + 52 and hence find the other three roots.

Real Analysis : Complex Power Series and Radius of Convergence

2. First do Problem #24 on p. 163 (as usual, using Problem 5 below to justify replacing roots by ratios in the definition of the radius of convergence). Then note that since the power series in question has radius of convergence 1, we can replace the real variable x with a complex variable z and then use the power series as the

Solutions to equation

Let lambda be real and lambda > 1, Show that the equation ze^lambda−z = 1 has exactly one solution in the disc |z| = 1, which is real and positive.

Complex Numbers, Standard Form and DeMoivre's Theorem

1. Evaluate the expression and write your answer in the form a+bi: i^100 2. Prove the following properties of complex numbers. 3. Find all solutions of equation:- 4. Find the indicated power using De Moivre's Theorem. .

Stereographic Projection

1. Let z and z' be points in C with corresponding points on the unit sphere Z and Z' by stereographic projection. Let N be the north pole N(0,0,1). a) Show that z and z' are diametrically opposite on the unit sphere iff z(z bar)'=-1 ps. here z bar means conjugate of z b) Show that the triangles Nz'z and NZZ' are similar. The

Projective geometry hyperplane

Projective Geometry Problem 4 Let C be the curve in a complex affine plane E. Find the infinite points of C, i.e. the points of the projective closure of that lie on the hyperplane at infinity. See attached file for full problem description.

Catenary Model

A) Graph the model b) Find the heights of the cable at the towers and at the midpoint between the towers, and c) Find the slope of the model at the point where the cable meets the right-hand tower y = 18 + 25cosh x/25, -25 ≤ x ≤ 25

Riemann Sums

Please see the attached file for the fully formatted problems.

Logarithms and Complex Numbers

1. Given that s = 1.59t(1-3v), obtain the value of v when s = 3.52 and t = 21.56. 2. Solve log(2x + 3) = log(4x) + 2, for x giving the answer correct to 3 significant figures. 3. For a thermodynamic process involving a perfect gas, the initial and final temperatures are related by: T1 exp(^s/Cp) =

Finding a Vertex and Vertex Form and Dividing Complex Numbers

1.Find the vertex form of the quadratic function g(T)=2T^2-4T+5 and determine the coordinates of this functions vertex vertex form_______________ the vertex______________ 2. solve problem following equations algebraically showing all work and steps and solutions -2X^4+6X^2-4=0 X=__________________ 3.showing all

Argand Diagram and Complex Impedance

Please see the attached file for full problem description. Show the following complex numbers on an Argand diagram: Given that the equivalent impedance of parallel complex impedances in an electric circuit is given by: calculate the equivalent impedance br the following circuit.

Question: complex number in polar form

(See attached file for full problem description) 1. simplify each of the following: giving your answer as a complex number in polar form: 2. Convert the following complex numbers in polar form to rectangular (a+jb) from:

Algebra: Complex Roots and Solutions, De Moivre's Theorem and Argand Diagrams

1 Find the real and complex solutions of these cubic equations. a) (z-3)(z2-5z+8)=0 b) z3 - 10z2- 34z- 40 = 0, given that 3-i is a root (solution). 2 Solve the equation z3 = 125 cis 45 3 Consider the complex number: z = = cos + z sin a) Use De Moivre's theorem to find z2, z4 and z6. Leave your answers in polar form. b) Pl

Complex numbers

Singularites (See attached file for full problem description)

Simplification

Indicate which answer is a simplification. (See attached file for full problem description)

Calculus

Question 1 Multiple Choice The two sides of a right triangle have lengths 2.92 and 3.98. Find the hypotenuse. □ 6.90 □ 3.34 □ 4.94 □ 3.20 Question 2 Multiple Choice An equation used in the study of protein molecule is In A+ In h - In(1 - h) Solve for