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**Unformatted text preview: **that d dz g ( z ) = f ( z )). Hint: The imaginary part of g can only be dened up to a constant. (4) Calculate the following integrals using the denition of contour integral: (a) H z n dz for n Z (also negative numbers!) and = C (0 , 1), the circle with center 0 and radius 1, traversed in a positive direction. (b) H z n dz for n Z and = C (2 , 1), again traversed in a positive direc-tion. (c) For | a | < r < | b | show that H 1 ( z-a )( z-b ) dz = 2 i a-b for = C (0 ,r ), traversed in positive direction. 1...

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