Complex Analysis: Theory and Applications · Problem 2.4.8

Analytic and Harmonic Functions — Howell & Matthews

Mathematics — Complex Analysis · nth-root-multivalued

Problem

Let f(z)=z1nf(z) = z^{\frac{1}{n}} denote the multivalued nnth root, where nn is a positive integer. (a) Show that ff is, in general, an nn-valued function. (b) Write the principal nnth root function. (c) Produce a different branch of the multivalued nnth root function.

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