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Thread: [SOLVED] Complex Analysis Proof

  1. #1
    Member ronaldo_07's Avatar
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    [SOLVED] Complex Analysis Proof



    How would I prove this?
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  2. #2
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    Write $\displaystyle f(x+iy) = u(x,y) + iv(x,y)$.
    We know that $\displaystyle v(x,y)=0$ by hypothesis.
    But, $\displaystyle u_x = v_y \implies u_x = 0 \implies u(x,y) = g(y)$.
    And, $\displaystyle u_y = -v_x \implies u_y = 0 \implies u(x,y) = h(x)$.
    Therefore, $\displaystyle g,h$ need to be constant functions.
    And so $\displaystyle u(x,y) = c$.
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