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 di²erentiable transformation f ( x, y ) = f ( z ) de±ned by f ( z ), considered as a function of two variables. 6. Suppose that f ( z ) is analytic in a connected domain Ω ⊂ C . Show that if f ( z ) is real for all z ∈ Ω, then f ( z ) must be a constant function on Ω . 1...
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This note was uploaded on 02/27/2012 for the course MATH 417 taught by Professor Staff during the Fall '11 term at SUNY Albany.
- Fall '11