In a question about harmonic and holomorphic functions in complex analysis, I was trying to expand $|f(x+iy)|^2 = 0$.
I did this by considering $f(z) = u(z) + iv(z)$ and applying the Laplacian operator on $u(z)^2+v(z)^2$ and then using Cauchy-Riemann equations to simplify.
However in the solutions it was directly given that $ \Delta |f(x+iy)|^2 = 4|′()|^2$. I am not sure how this was given directly as there were no other steps.
Why is this step true?