- #1

- 158

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By the Cauchy-Riemann equations,

[tex]u_x = \frac{x}{\sqrt{x^2+y^2}}[/tex]

[tex]v_y = -v_x = 0[/tex]

[tex]u_y = \frac{y}{\sqrt{x^2+y^2}}[/tex]

Since the C.R. equations don't work at (0,0), how can show [itex]f(z)[/itex] is not holomorphic at (0,0)?