Unformatted text preview: that d dz g ( z ) = f ( z )). Hint: The imaginary part of g can only be deﬁned up to a constant. (4) Calculate the following integrals using the deﬁnition of contour integral: (a) H γ z n dz for n ∈ Z (also negative numbers!) and γ = C (0 , 1), the circle with center 0 and radius 1, traversed in a positive direction. (b) H γ z n dz for n ∈ Z and γ = C (2 , 1), again traversed in a positive direction. (c) For  a  < r <  b  show that H γ 1 ( za )( zb ) dz = 2 πi ab for γ = C (0 ,r ), traversed in positive direction. 1...
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 Spring '09
 Derivative, Polar Coordinates, Holomorphic function, positive direction, ∂u ∂v ∂u

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