I am trying to show that assuming for an analytic $f$ we have $|f|$ is also analytic. That the original f must be constant.
My original thought was to use the Cauchy Riemann equations to try and show that the partial derivatives are equal to their negatives. I am unsure how to carry this out however, as I am struggling to express the partial derivatives of $|f|$ in terms of the partial derivatives of $f$.
Could someone please let me know if I'm on the right track, or else give me a nudge in the correct direction.
Thanks in advance