$$f(a)=\int_{\gamma\ \ \ \ \ }^{ }\ \frac{f\left(z\right)}{z-a}dz$$ is known as

Winding number of a with respect to $$\gamma$$

Find the pole(s) for the function $$f\left(z\right)=\frac{z^2}{\left(z+1\right)\left(z-2\right)}$$

The poles are z = -1 and z = 2.

The poles are z = 1 and z = -2.

The poles are z = -1 and z = -2.

In which place, the maximum value of modulus of $$f\left(z\right)$$ attains?

Boundary of closed and bounded set E

Interior of closed and bounded set E

Choose the correct statement(s)

The number of zeros enclosed by $$\gamma$$ is the winding number of 0 with respect to image of $$\gamma$$

The number of zeros of $$f\left(z-a\right)$$ enclosed by $$\gamma$$ is the winding number of a with respect to the image of $$\gamma$$

The number of zeros enclosed by $$\gamma$$ is the winding number of 0 with respect to $$\gamma$$

The number of zeros of $$f\left(z-a\right)$$ enclosed by $$\gamma$$ is the winding number of a with respect to $$\gamma$$

Which of the following statement is/ are false?

A non constant function maps open onto open sets

If $$f\left(z\right)$$ is analytic at $$z$$ , then it maps a neighbourhood of $$z$$ conformally and topologically onto a region

Any analytic and bounded function must reduce to a constant

$$f_n\left(z\right)=\frac{1}{2\pi i}\int_C^{ }\ \ \frac{f\left(\xi\right)}{\left(\xi-a\right)^n\ \left(\xi-z\right)}d\xi$$ is the representation for $$f_n\left(z\right)$$

Choose the characterization for a region $$\Omega$$ to be simply connected

Winding number $$n\left(\gamma,\ a\right)=0$$ for all cycles $$\gamma$$ in $$\Omega$$ and for all the point $$a$$ does not belong to $$\Omega$$

Winding number $$n\left(\gamma,\ a\right)=0$$ for all the point $$a$$ belong to $$\Omega$$

Winding number $$n\left(\gamma,\ a\right)=0$$ for all cycles $$\gamma$$ in $$\Omega$$ and for all the point $$a$$ belong to $$\Omega$$

Winding number $$n\left(\gamma,\ a\right)=0$$ for all cycles $$\gamma$$ in $$\Omega$$

What is meant by zero sum in a chain?

sum of all coefficients equal to zero

at least one of the coefficient equal to zero

sum of all coefficients equal to zero

Choose the correct statement(s)

sum of closed curves is a cycle

a region without hole is simply connected

If $$f\left(z\right)$$ is analytic in $$\Omega$$ , then $$\int_{\Upsilon}^{ }\ f\left(z\right)dz=0$$ for every cycle $$\gamma$$ which is homologous to zero in $$\Omega$$ . This statement is known as

Generalization of Cauchy's Theorem

Cauchy's Theorem for Closed Curves

Complex Analysis (MP233CC1) - Quiz 1

Authored by Anat A

Mathematics

University

Used 3+ times

AI Actions

Add similar questions

Adjust reading levels

Convert to real-world scenario

Translate activity

More...

Content View

Student View

20 questions

Show all answers

MULTIPLE SELECT QUESTION

5 mins • 1 pt

Which of the following is/are correct?

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

The curves will have different lengths.

The curves will have different shapes.

The net area enclosed by both curves will be infinite.

The area enclosed by both curves will be zero.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

True or False: The integral value of any analytic function in the rectangle R is zero.

True

False

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

True

False

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

4πi

πi

3πi

2πi

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

The winding number of a point inside the circle is

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Representation Formula

Cauchy Integral Formula

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Continue with Google

Continue with Email

Continue with Classlink

Continue with Clever

or continue with

Microsoft

Apple

Others

Already have an account?

Similar Resources on Wayground

20 questions

Eng Math 1, QB1 - Vectors

Quiz

•

University

16 questions

Illustrating and Probability of Event

Quiz

•

10th Grade - University

16 questions

Malaysia Day Quiz Section 3

Quiz

•

University

15 questions

319

Quiz

•

3rd Grade - University

20 questions

DERIVATIVE REVIEW (3 STEP)

Quiz

•

10th Grade - University

17 questions

8th Grade Unit 4 Pre-Test/Study Guide

Quiz

•

8th Grade - University

20 questions

quiz 3

Quiz

•

7th Grade - University

15 questions

Average Round Quiz Bee - IMD

Quiz

•

University

Popular Resources on Wayground

15 questions

Fractions on a Number Line

Quiz

•

3rd Grade

20 questions

Equivalent Fractions

Quiz

•

3rd Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

54 questions

Analyzing Line Graphs & Tables

Quiz

•

4th Grade

$fractions$

22 questions

fractions

Quiz

•

3rd Grade

20 questions

Main Idea and Details

Quiz

•

5th Grade

20 questions

Context Clues

Quiz

•

6th Grade

15 questions

Equivalent Fractions

Quiz

•

4th Grade

Discover more resources for Mathematics

20 questions

Ch. 7 Quadrilateral Quiz Review

Quiz

•

KG - University

7 questions

Introduction to Fractions

Interactive video

•

1st Grade - University

18 questions

Exam Review

Quiz

•

University

16 questions

Parallel, Perpendicular, and Intersecting Lines

Quiz

•

KG - Professional Dev...

25 questions

Math College Placement Practice #2

Quiz

•

11th Grade - University

10 questions

One Step Equations Multiply and Divide

Quiz

•

University

Complex Analysis (MP233CC1) - Quiz 1

Which of the following is/are correct?

True or False: The integral value of any analytic function in the rectangle R is zero.

The winding number of a point inside the circle is

The value of Cauchy's Estimate is

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics