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Calculate imaginary part if real part is following

  1. Feb 14, 2014 #1
    1. The problem statement, all variables and given/known data
    [tex]f:\ v(x,y)=4xy+2x[/tex]

    The task is to calculate the imaginary part.


    2. Relevant equations



    3. The attempt at a solution

    I have no idea what to do because in my opinion u(x,y) can be anything. For example: [tex]f(x,y)=4xy+2x+(3x-4y)\text i[/tex]. But I must be wrong. I would appreciate if you just tell me what to do or where is my mistake, because I want to solve it alone :)
     
  2. jcsd
  3. Feb 14, 2014 #2
    Read some information on the Cauchy Riemann equations
     
  4. Feb 14, 2014 #3

    vanhees71

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    Science Advisor
    2016 Award

    Well, usually one writes
    [tex]f(z)=f(x+\mathrm{i} y)=u(x,y)+\mathrm{i} v(x,y).[/tex]
    If you now assume that [itex]f[/itex] is a analytic function, you have the Cauchy-Riemann differential equations, relating the real and imaginary parts
    [tex]\partial_x u=\partial_y v, \quad \partial_y u=-\partial_x v.[/tex]
    So if you have given [itex]u[/itex] (real part) you can determine the imaginary part (up to a constant) and vice versa.

    Read the question carefully again, because it seems as if the imaginary part is given and you look for the real part and not the other way around.
     
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