Given n > 1, define f(z) = 1/z" for z + 0. Show that f(z) = U(r,0) + iV(r,0) for U(r, 0) = cos(no) V (r, 0) sin(no) - pn pn Deduce that f(z) is holomorphic on the open set A= C \ {0} with n f'(z) = Vz...

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Extracted text: Given n > 1, define f(z) = 1/z" for z + 0. Show that f(z) = U(r,0) + iV(r,0) for U(r, 0) = cos(no) V (r, 0) sin(no) - pn pn Deduce that f(z) is holomorphic on the open set A= C \ {0} with n f'(z) = Vz E A. zn+1