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**Unformatted text preview: **are analytic functions on U with f ( z ) 6 = 0 for all z ∈ U . Let’s define the multi-valued function ( f ( z ) ) g ( z ) := exp( g ( z ) log f ( z )) . 1. Show at an example (i.e. your choice of f and g ) that in general this function is multi-valued. 2. Show at another example (i.e. again your choice of f and g ) that this function may be single-valued. 3. Now suppose z ∈ C with Arg f ( z ) 6 = π . Construct a neighborhood of z and a branch of ( f ( z ) ) g ( z ) in this neighborhood. 4. Compute the derivative of this branch. 1...

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- Fall '07
- Lim
- Complex Numbers, Complex number