Let a≠0 be a complex number, and define the αth branch of zª by f(z) := exp(aLogα(z)). Show that, for z € C \ Rα, we have ƒ'(z)

Question

Let a≠0 be a complex number, and define the αth branch of zª by f(z) := exp(aLogα(z)). Show that, for z € C \ Rα, we have ƒ'(z) = af(z)/z. This means d/dzzª= aza-1 where we pick the same branch on both sides of the identity.

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