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# Complex anaylsis, cite all theorems used. Y are one Consider the real valued function ulx,y) with...

## Question

###### Complex anaylsis, cite all theorems used. Y are one Consider the real valued function ulx,y) with...

Complex anaylsis, cite all theorems used.

Y are one Consider the real valued function ulx,y) with x and real variables. For each definition of ucxy) below, find whether there cette exists real-valued function v(x,y) such that f(2)= u(x, y) tivcx,y) is a function analytic in some DEC. If such such v(x,y) and determine V(X,Y) the domain of analyticity D for fcz). It such a not exist, prove that it does not exist. (i) u (x,y)= xy2-x²y (ii) ucx, y) = y3 - 3x²4 Gm ulx,y)= Arg (xtiys exists, find ucxys does

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