Editing Maximum modulus principle (section)

===Using the maximum principle for harmonic functions===
One can use the equality

:<math>\log f(z) = \ln |f(z)| + i\arg f(z)</math>

for complex [[natural logarithm]]s to deduce that <math> \ln |f (z) | </math> is a [[harmonic function]]. Since <math>z_0</math> is a local maximum for this function also, it follows from the [[maximum principle]] that  <math>| f (z) | </math>  is constant. Then, using the [[Cauchy–Riemann equations]] we show that <math>f'(z)</math> = 0, and thus that <math>f(z)</math> is constant as well. Similar reasoning shows that  <math> | f (z) | </math>  can only have a local minimum (which necessarily has value 0) at an isolated zero of <math>f(z)</math>.