All Complex Analysis Resources
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 #1 : 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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