Question: Let a?0 be a complex number, and define the ?th branch of z by f(z) := exp(aLog?(z)). Show that, for z C R?,

Let a?0 be a complex number, and define the ?th branch

of zª by f(z) := exp(aLog?(z)). Show that, for z € C

Let a?0 be a complex number, and define the ?th branch of zª by f(z) := exp(aLog?(z)). Show that, for z € C \ R?, 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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