Complex Integration
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Complex Analysis › Complex Integration
Questions 1 - 2
1
Let be the region of the complex plane enclosed by
Compute
Explanation
Recall Cauchy's integral formula, which states
In this case, we have
Plugging in gives us
2
Let be the unit circle.
Compute
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