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**sashikanth** Let $\displaystyle f(z) = z^2 - z $ in the circular region $\displaystyle R = {z: |z| \leq 1} $. Find points in $\displaystyle R $ where $\displaystyle |f(z)| $ has its maximum or minimum values.

An attempt at a solution: Use $\displaystyle z = x+iy $ to convert the given function into one in x and y, and then take the norm using the standard formula and differentiate partially wrt x, y to get extrema points.

The problem is that the resulting function of x, y is too cumbersome and when I differentiate and try to solve the 2 resulting equations, I am unable to solve it. Is there any other approach to solve such problems?