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If $f:U\subset\mathbb{C}\mapsto\mathbb{C}$, where $f(x+iy)=u(x,y)+iv(x,y)$ is a meromorphic function and if $f$, f', and f'' are not zero in the strip $a, can we get $\frac{\partial}{\partial x}|f|^2$ is not zero?

thanks

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Try $f(z) = e^{iz}$, noting that $|f(z)| = e^{-y}$