Is this a valid exercise?












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In Needham's Visual Complex analysis he sets the following exercise - Chapter 12 ex 12(i) on page 571:



Consider the image under an analytic mapping $f$ of a source of strength $S$ located at $p$.



(i) show geometrically, then algebraically, that if $p$ is not a critical point of $f$ (i.e., $f'(p)neq 0$) then the image is another source of strength $S$ at $f(p)$.



[A source of this type is given by $V=(S/2pi)(1/(overline{z}-overline{p})$]



I don't want a solution to the exercise because I want to try it myself, but I'm not convinced that it's a valid exercise because if $f$ is a general analytic function how can we be so specific about the image of the mapping?






complex-analysis







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    0












    $begingroup$


    In Needham's Visual Complex analysis he sets the following exercise - Chapter 12 ex 12(i) on page 571:



    Consider the image under an analytic mapping $f$ of a source of strength $S$ located at $p$.



    (i) show geometrically, then algebraically, that if $p$ is not a critical point of $f$ (i.e., $f'(p)neq 0$) then the image is another source of strength $S$ at $f(p)$.



    [A source of this type is given by $V=(S/2pi)(1/(overline{z}-overline{p})$]



    I don't want a solution to the exercise because I want to try it myself, but I'm not convinced that it's a valid exercise because if $f$ is a general analytic function how can we be so specific about the image of the mapping?






    complex-analysis







    share|cite|improve this question











    $endgroup$















      0












      0








      0





      $begingroup$


      In Needham's Visual Complex analysis he sets the following exercise - Chapter 12 ex 12(i) on page 571:



      Consider the image under an analytic mapping $f$ of a source of strength $S$ located at $p$.



      (i) show geometrically, then algebraically, that if $p$ is not a critical point of $f$ (i.e., $f'(p)neq 0$) then the image is another source of strength $S$ at $f(p)$.



      [A source of this type is given by $V=(S/2pi)(1/(overline{z}-overline{p})$]



      I don't want a solution to the exercise because I want to try it myself, but I'm not convinced that it's a valid exercise because if $f$ is a general analytic function how can we be so specific about the image of the mapping?






      complex-analysis







      share|cite|improve this question











      $endgroup$




      In Needham's Visual Complex analysis he sets the following exercise - Chapter 12 ex 12(i) on page 571:



      Consider the image under an analytic mapping $f$ of a source of strength $S$ located at $p$.



      (i) show geometrically, then algebraically, that if $p$ is not a critical point of $f$ (i.e., $f'(p)neq 0$) then the image is another source of strength $S$ at $f(p)$.



      [A source of this type is given by $V=(S/2pi)(1/(overline{z}-overline{p})$]



      I don't want a solution to the exercise because I want to try it myself, but I'm not convinced that it's a valid exercise because if $f$ is a general analytic function how can we be so specific about the image of the mapping?






      complex-analysis




      complex-analysis






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Jan 27 at 19:20







      Ian Taylor

















      asked Jan 27 at 16:30









      Ian TaylorIan Taylor

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