Problem

Find a nonconstant complex function f that is nowhere analytic but is differentiable on th...

Find a nonconstant complex function f that is nowhere analytic but is differentiable on the unit circle |z| = 1. [Hint: Consider using a function f similar to the one in Problem 1.]

Problem 1

Suppose g(x) is a twice differentiable real function and f is a complex function defined by f(z) = g(x) + iy2. Determine where f(z) is differentiable and where it is analytic. Where did you use the hypothesis that g is twice differentiable?

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Solutions For Problems in Chapter 3.3