What is the Value of given integral if:a) C is the circle Iz+iI=1b) if C is an eclipse x2+2y2=8 What is the value of322 + 7z +1z +1dz

Given integral is I=∮C3z2+7z+1z+1. (a) The given curve C is the circle z+i=1. (b) The given curve C…

Answered: What is the value of [ 32² +7z+1dz 2+1…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter1: Variables, Expressions, And Integers

Section1.3: Order Of Operations

Problem 9C

See similar textbooks

Related questions

Question

What is the Value of given integral if:

a) C is the circle Iz+iI=1

b) if C is an eclipse x²+2y²=8

What is the value of
322 + 7z +1
z +1
dz

Expert Solution

Step 1

Given integral is $I = \oint_{C} \frac{3 z^{2} + 7 z + 1}{z + 1}$ .

(a) The given curve $C$ is the circle $|z + i| = 1$ .

(b) The given curve $C$ is an ellipse $x^{2} + 2 y^{2} = 8$ .

We know that if a function $f (z)$ is analytic over a closed contour $C$ , then $\oint_{C} f (z) d z = 0$ .

We know that if $C$ is simple closed contour and $f (z)$ is analytic except at $z_{0}$ inside $C$ , then $\oint_{C} f (z) d z = 2 {πiRes}_{f} (z_{0})$ .

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

Recommended textbooks for you

Holt Mcdougal Larson Pre-algebra: Student Edition…

Algebra

ISBN:

9780547587776

Author:

HOLT MCDOUGAL

Publisher:

HOLT MCDOUGAL

Algebra: Structure And Method, Book 1

Algebra

ISBN:

9780395977224

Author:

Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:

McDougal Littell

Elementary Algebra

Algebra

ISBN:

9780998625713

Author:

Lynn Marecek, MaryAnne Anthony-Smith

Publisher:

OpenStax - Rice University

Holt Mcdougal Larson Pre-algebra: Student Edition…

Algebra

ISBN:

9780547587776

Author:

HOLT MCDOUGAL

Publisher:

HOLT MCDOUGAL

Algebra: Structure And Method, Book 1

Algebra

ISBN:

9780395977224

Author:

Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:

McDougal Littell

Elementary Algebra

Algebra

ISBN:

9780998625713

Author:

Lynn Marecek, MaryAnne Anthony-Smith

Publisher:

OpenStax - Rice University

Glencoe Algebra 1, Student Edition, 9780079039897…

Algebra

ISBN:

9780079039897

Author:

Carter

Publisher:

McGraw Hill

College Algebra

Algebra

ISBN:

9781305115545

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

Intermediate Algebra

Algebra

ISBN:

9780998625720

Author:

Lynn Marecek

Publisher:

OpenStax College

SEE MORE TEXTBOOKS

What is the value of [ 32² +7z+1dz 2+1 C