Let in the circular region . Find points in where has its maximum or minimum values.

An attempt at a solution: Use 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?