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    Complex Analysis / Argument Principle : Analyticity, Solutions and Multiplicities

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    Suppose f is analytic on B(bar) (0;1) and satisfies |f(z)| < 1 for |z| = 1. Find the number of solutions (counting multiplicities) of the equation f(z) = z^n, where n is an integer larger than or equal to 1.

    Please justify every step and claim and refer to any theorems you use.

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    Solution Summary

    Analyticity, solutions and multiplicities are investigated.