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Unformatted text preview: ( x, y ). Since f is analytic, we know that u and v have continuous partial derivatives and u x = v y , u y =v x . If we dene f * ( z ) = f ( z ), then we have f * ( z ) = u * ( x, y ) + iv * ( x, y ) with u * ( x, y ) = u ( x,y ) and v * ( x, y ) =v ( x,y ). We compute u * x ( x, y ) = u x ( x,y ) = v y ( x,y ) , u * y ( x, y ) =u y ( x,y ) = v x ( x,y ) , v * x ( x, y ) =v x ( x,y ) , v * y ( x, y ) = v y ( x,y ) , and therefore u * x = v * y and u * y =v * x . This shows that f * is analytic. 1...
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 Three '09
 Cong
 Geometry

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