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If I solve a complex f(z)=u(x,y) + iv(x,y), I determine its analytic by using Cauchy Riemann method du/dx = dv/dy and -du/dy = dv/dx. But I find a expression of y in term of x in order to satisfy the Cauchy Riemann, is f(z) still considered as analytic? Thx for answering first.