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Complex Analysis

Cavalieri's principle

Please see the attached document for homework specifics. Thank-you for your help. Using Cavalieri's principle, compute the volume of the structure...

Isolated singularities

Please show all steps to solution. See attached Classify with proof all the isolated singularities in C of ...

Complex Variables : The Minimum Principle

Please see the attached file for the fully formatted problem. The Minimum Principle: Let f be analytic in a bounded region D and continuous and nonzero on bar-D. Show that |f(z)| attains its minimum on the boundary of D. Hint: Consider the function g(z) =1/f(z).

Radicals and complex numbers

Attached 16.) Simplify 17.) Add the complex numbers 2+3i and -3+i 18.) Divide the complex number 2+1 by the complex number 3-i 19.) Factor 20.) Simplify:

Complex numbers

I have attached the problem. Z1=3-5i Z2=2+1 Z3=1+4i Find Z1+Z2-Z3 Z2-5Z3 Z1*Z3 Z2/Z3

Volume of Revolution Problem

Please see the attached file for the complete problem. Find the volume of the solid of revolution formed by rotating the finite region bounded by the graphs of y=sin((pi)x^2)/2) and y=x^5 about the y-axis. The possible answers are: A. 2(5pi-7)/7 B. (7pi-5)/7 C. 2(5-pi)/7 D. (5pi+2)/7 E. 2(7-pi)/7

Complex Variables

Please show all steps to solution. Suppose that P is a polynomial with no roots on the contour Y .Show that the number of roots of P in the region enclosed by Y is given by

Complex Variables

Please show all steps to solution (see attached) Let be the curve parameterized by ζ(t) = for Evaluate the integral dz

Euler's equation

Show that y=(A*e^ix)+(B*e^-ix) can be written as y=C*cosine(x-g) A and B are complex but C and g are real Please show all steps!

Complex Analysis

Please show all logic leading up to answer. Find the image of D = under the map w =

Intermediate value theorem

See attached for circled problems Suppose that a function f is continuous on [0,1] except at 0.25 and that f(0)=1 and f(1)=3..... Use the Intermediate Value Theorem to show that there is a root of the given equation on the interval specified.

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)

Complex analysis

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).

Combinatorial Analysis

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

Mathematicians say that division by zero is forbidden.

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

Determine if the following equations are real or complex.

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

Complex Inner-Product Space : Complex Spectral Theorem

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

Parabolas and Complex Roots

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,

Are the roots real, repeated real, or complex?

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

Solve the triangle and complex number

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.