Question: Let f : U C be a function, where U C is open. We denote by u(x, y) and v(x, y) the real and imaginary

Let f : U C be a function, where U C is open. We denote by u(x, y) and v(x, y) the real and imaginary parts of f, i.e., f(x + iy) = u(x, y) + iv(x, y). The Jacobian of f is given by Jf = uxvy uyvx.

(i) Show that Jf = |f'|2 whenever f is holomorphic.

(ii) Find a function f : C C such that Jf = 1 on C. Why does this show that f is not holomorphic

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