Complex Analysis : Complex Integration

Study concepts, example questions & explanations for Complex Analysis

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Example Questions

Example Question #1 : Complex Integration

Let  be the region of the complex plane enclosed by 

Compute 

Possible Answers:

Correct answer:

Explanation:

Recall Cauchy's integral formula, which states

In this case, we have 

Plugging in gives us

Example Question #2 : Complex Integration

Let be the unit circle. 

Compute 

Possible Answers:

Correct answer:

Explanation:

Recall the Taylor expansion of 

 

Use this to write

The coefficient of  is the residue, so by the residue theorem, the value of the integral is 

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