solved Show that f(z) = |z|^2 is differentiable only at z=0

Question : Show that f(z) = |z|^2 is differentiable only at z=0Solution :Given complex functionf(z) = |z|^2 = z z ̅Since z= x+iy and z ̅= x-iy, i^2=-1 f(z) =u(x,y)+iv(x,y)= x^2 + y^2u=x^2+y^2, v=0Therefore their partial derivatives are∂u/∂x = 2x, ∂u/∂y = 2y,…

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