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.
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