Civil Engineering (CE) Exam > Civil Engineering (CE) Questions > Let f(z) =if C is a counter clock wise path i...
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Let f(z) = 
if C is a counter clock wise path in the z plane such that |z - i| = 2, then the value of 
is____
if C is a counter clock wise path in the z plane such that |z - i| = 2, then the value of is____- a)0
- b)1
- c)π/2
- d)-π
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Let f(z) =if C is a counter clock wise path in the z plane such that |...
Concept:
Cauchy’s Theorem:
If f(z) is an analytic function and f’(z) is continuous at each point within and on a closed curve C, then
Calculation:
Given:
C: |z - i| = 2
The above path is a circle with a radius of 2 and center as (0, 1). The graph of the circle is given below,
⇒ After putting the denominator as zero, the poles will be 'z = ± πi '. These pole points A and B are outside of the given circle as shown above. So, the complex function f(z) will be an analytic function for all points inside the circle.
⇒ After putting the denominator as zero, the poles will be 'z = ± πi '. These pole points A and B are outside of the given circle as shown above. So, the complex function f(z) will be an analytic function for all points inside the circle.
By Cauchy’s Theorem (Using equation (1))
Most Upvoted Answer
Let f(z) =if C is a counter clock wise path in the z plane such that |...
Concept:
Cauchy’s Theorem:
If f(z) is an analytic function and f’(z) is continuous at each point within and on a closed curve C, then
Calculation:
Given:
C: |z - i| = 2
The above path is a circle with a radius of 2 and center as (0, 1). The graph of the circle is given below,
⇒ After putting the denominator as zero, the poles will be 'z = ± πi '. These pole points A and B are outside of the given circle as shown above. So, the complex function f(z) will be an analytic function for all points inside the circle.
⇒ After putting the denominator as zero, the poles will be 'z = ± πi '. These pole points A and B are outside of the given circle as shown above. So, the complex function f(z) will be an analytic function for all points inside the circle.
By Cauchy’s Theorem (Using equation (1))
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Question Description
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