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Analytic real world functions

Which of the following real functions u(x,y) of two real variables are the real parts of an analytic function f(z) with z=x+iy

a) u(x,y) = x^3-y^3

b) u(x,y)=x^2-y^2+y

IN each case compute f(z) if it exists

Solution Summary

This provides an example of determining if functions are parts of analytic functions.