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Analytic function problem

  1. Sep 14, 2008 #1
    1. The problem statement, all variables and given/known data
    Apply rules of Cauchy-riemann theory to verify that each of these functions is entire:

    f(z)=3*x+y+i(3y-x)



    2. Relevant equations

    u_x=v_y, u_y=-v_x

    3. The attempt at a solution

    u(x,y)=3x+y
    v(x,y)=3y-x

    u_x=3
    v_y=3
    u_y=1
    -v_y=1
    I know that a function is analytic at each point, then the function is entire. How would I show that the function is analytic at each pt.?
     
  2. jcsd
  3. Sep 14, 2008 #2

    Dick

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    Science Advisor
    Homework Helper

    You've shown it satisfies CR everywhere. The only thing that could prevent it from being entire is if it has a removable singularity someplace. Does it? Does it have ANY singularities?
     
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