Question

determine the analytic function whose real part is log √ײ + y²


answer fast! ​

Answer 1

Answer:

Step-by-step explanation:

I would like to show that log(x2+y2) is not the real part of any analytic function in C−{0} A similar question can be found here, but I don't think this argument is satisfactory.

Here are my thoughts on the problem. On the domain C−{x≥0}, log(x2+y2)=Re(log(z2)). Therefore, if I can show the only analytic function with real part log(x2+y2) is log(z2) then the problem is solved, since log(z2) is not analytic on the positive real-axis. The problem I have is I don't know how to show that the only analytic function with real part log(x2+y2) is log(z2)