Question

Show that an analytic function of constant absolute value is constant

Answer 1

Answer:

What I was thinking is to use Cauchy-Riemann equations, but it didn't work well...

If this is not true, I would like to know the counterexample...

Here is what I tried:

|f|=|u+iv|=u2+v2−−−−−−√

Thus u2+v2 is a constant.

(1) uδuδx+vδvδx=0

(2) uδuδy+vδvδy=0