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Unformatted text preview: | f ( z ) | 2 = u x v y u y v x Hence, the absolute value of the derivative of an analytic function f ( z ) is the Jacobian of the dierentiable transformation f ( x, y ) = f ( z ) dened by f ( z ), considered as a function of two variables. 6. Suppose that f ( z ) is analytic in a connected domain C . Show that if f ( z ) is real for all z , then f ( z ) must be a constant function on . 1...
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- Fall '11