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Math Help - [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 f(x+iy) = u(x,y) + iv(x,y).
    We know that v(x,y)=0 by hypothesis.
    But, u_x = v_y \implies u_x = 0 \implies u(x,y) = g(y).
    And, u_y = -v_x \implies u_y = 0 \implies u(x,y) = h(x).
    Therefore, g,h need to be constant functions.
    And so u(x,y) = c.
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