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Complex analysis

  1. Aug 18, 2008 #1

    I want to find an analytic funktion if Re(z) = 1 - x - 2xy

    My initial thought was to set U(x,y) = 1 - x - 2xy and then solve for V(x,y) through
    du/dx = dv/dy but it doesnt seem to go as far as im concernd.

    Then I thought about the fact that Re(z) = (z + zbar)/2 and then work from there but I cant figure out how.

    My book says: 1 - z + iz^2 + iC, CeR
  2. jcsd
  3. Aug 18, 2008 #2


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    Riemember the Riemann conditions: if f(x+ iy)= u(x,y)+ iv(x,y) then
    [tex]\frac{\partial u}{\partial x}= \frac{\partial v}{\partial y}[/tex]
    [tex]\frac{\partial u}{\partial y}= -\frac{\partial v}{\partial x}[/tex]

    If Re(f(z))= u(x,y)= 1- x- 2xy, then
    [tex]\frac{\partial u}{\partial x}= \frac{\partial v}{\partial y}= -1- 2y[/tex]
    [tex]\frac{\partial u}{\partial y}= -\frac{\partial v}{\partial x}= -2x[/tex]
    You can find v from that. There are many correct answers.
  4. Aug 18, 2008 #3
    ok I got it! ty...I was alittle confused by the answer.
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