Let zo (20. Yo) E C and assume that f'(zo) exists. Use polar coordinates r=rcos 0,...
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Let zo (20. Yo) E C and assume that f'(zo) exists. Use polar coordinates r=rcos 0, y = r sine and the chain rule to conclude that f'(20) = = e(u,+ iv) (ro,00) Furthermore, conclude that the Cauchy-Riemann equations can be written as: Tur= Vo, Ug=-TV. Show that f'(z) does not exist at any point if f(2)=ž, f(z) = Rez, f(z) = 2x +ixy². Let zo (20. Yo) E C and assume that f'(zo) exists. Use polar coordinates r=rcos 0, y = r sine and the chain rule to conclude that f'(20) = = e(u,+ iv) (ro,00) Furthermore, conclude that the Cauchy-Riemann equations can be written as: Tur= Vo, Ug=-TV. Show that f'(z) does not exist at any point if f(2)=ž, f(z) = Rez, f(z) = 2x +ixy².
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To show that fz 0 in polar coordinates and that the CauchyRiemann equations can be written as equations in polar form well first apply the chain rule ... View the full answer
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