I have a question regarding Cauchy Integral formula,
I was given an assignment questions, and my professor uploaded a solution and i do not understand how he reached to an answer with his method. Can anyone provide me with a clearer method? [Part 2]
2026-04-03 00:57:18.1775177838
Question regarding Cauchy Integral formula
133 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in COMPLEX-ANALYSIS
- Minkowski functional of balanced domain with smooth boundary
- limit points at infinity
- conformal mapping and rational function
- orientation of circle in complex plane
- If $u+v = \frac{2 \sin 2x}{e^{2y}+e^{-2y}-2 \cos 2x}$ then find corresponding analytical function $f(z)=u+iv$
- Is there a trigonometric identity that implies the Riemann Hypothesis?
- order of zero of modular form from it's expansion at infinity
- How to get to $\frac{1}{2\pi i} \oint_C \frac{f'(z)}{f(z)} \, dz =n_0-n_p$ from Cauchy's residue theorem?
- If $g(z)$ is analytic function, and $g(z)=O(|z|)$ and g(z) is never zero then show that g(z) is constant.
- Radius of convergence of Taylor series of a function of real variable
Related Questions in COMPLEX-NUMBERS
- Value of an expression involving summation of a series of complex number
- Minimum value of a complex expression involving cube root of a unity
- orientation of circle in complex plane
- Locus corresponding to sum of two arguments in Argand diagram?
- Logarithmic function for complex numbers
- To find the Modulus of a complex number
- relation between arguments of two complex numbers
- Equality of two complex numbers with respect to argument
- Trouble computing $\int_0^\pi e^{ix} dx$
- Roots of a complex equation
Related Questions in COMPLEX-INTEGRATION
- Contour integration with absolute value
- then the value of $ \frac{1-\vert a \vert^2}{\pi} \int_{\gamma} \frac{\vert dz \vert}{\vert z+a \vert^2} $.
- Checking that a function is in $L^p(\mathbb{C})$
- Calculate integral $\int_{0}^{2\pi} \frac{dx}{a^2\sin^2x+b^2\cos^2x}$
- Complex integral of $\cfrac{e^{2z}}{z^4}$
- Have I solved this complex gaussian integral correctly?
- Evaluate the integral $ I=\frac{1}{2\pi i}\int_{\vert z \vert =R}(z-3)\sin \left(\frac{1}{z+2}\right)dz$,
- Integrating using real parts
- Complex integral(s)of Hyperbolic functions for different contours
- Are the Poles inside the contour?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
HINT:
The solutions to $z^{10}+2=0$ are found as
$$z^{10}=-2\implies z^{10}=2e^{i(2n+1)\pi}\implies z=2^{1/10}e^{i(2n+1)\pi/10}\implies |z|=2^{1/10}<2$$
Thus, all roots of $z^{10}+2=0$ lie within the region $|z|<2$. Therefore, the poles of $\frac{z^{10}}{(z-1/2)(z^{10}+2)}$ are at $z=1/2$ and $z=2^{1/10}e^{\pm i(2n+1)\pi/10}$ for $n=0,1,2,3,4$.