CalcIVComplexPractice

CalcIVComplexPractice - 1 2 + i to 1 2-i . If f ( z ) = 2 e...

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Sample questions for complex integration 1. Let C be the curve z ( t ) = t 2 + it 3 for 0 t 1, and let f ( z ) = e πiz . Compute R C f ( z ) dz . 2. Let C be the line segment from i to 1, and let f ( z ) = z · z . Compute R C f ( z ) dz . 3. Let C be the curve consisting of the line segment from 1 2 - i to 2 - i , followed by the segment from 2 - i to 2 + i , followed by the segment from 2 + i to 1 2 + i , followed by the segment from
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Unformatted text preview: 1 2 + i to 1 2-i . If f ( z ) = 2 e z z 2-z , compute R C f ( z ) dz . (Hint: Write f ( z ) as g ( z ) / ( z-z ) and use Cauchys integral formula.) 4. Let C be the unit circle, and suppose that f ( x + iy ) = x + iy on C . If f ( z ) is holomorphic on C , what is f (0)? 1...
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This note was uploaded on 07/25/2008 for the course MATH V1202 taught by Professor Neel during the Spring '07 term at Columbia.

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