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I am trying to think of a complex function that is nowhere differentiable except at the origin and on the circle of radius 1, centered at the origin. I have tried using the Cauchy-Riemann equations (where f(x+iy)=u(x,y)+iv(x,y))

[tex]

\frac{\partial u}{\partial x}=\frac{\partial v}{\partial y} \qquad \quad \frac{\partial v}{\partial x}=-\frac{\partial u}{\partial y}

[/tex]

to reduce it to a set of differential equations, but I haven't had any luck. Any suggestions on how to go about this? Thanks in advance for any input.

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# Differentiability of a complex function.

Can you offer guidance or do you also need help?

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