7.10. In polar coordinates r = r cos 0, y =r sin 0, the function f(z) = u(r, 0) +iv(r, 0). Show that the Cauchy-Riemann conditions can be written as du 1 dv 1 ди dv (7.7) dr r d0 r d0 ar and f'(2)...

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Extracted text: 7.10. In polar coordinates r = r cos 0, y =r sin 0, the function f(z) = u(r, 0) +iv(r, 0). Show that the Cauchy-Riemann conditions can be written as du 1 dv 1 ди dv (7.7) dr r d0 r d0 ar and f'(2) e-i° (ur + iv,). (7.8) In particular, show that f(z) = Vreie/2 is differentiable at all z except z = 0 and f'(2) = (1/2/F)e¬i®/2.