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2011 PUMaC Algebra B4

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September 24, 2019
algebra

Problem Statement

Let ff be an invertible function defined on the complex numbers such that z2=f(z+f(iz+f(−z+f(−iz+f(z+…)))))z^2 = f(z + f(iz + f(-z + f(-iz + f(z + \ldots))))) for all complex numbers zz. Suppose z0≠0z_0 \neq 0 satisfies f(z0)=z0f(z_0) = z_0. Find 1/z01/z_0. (Note: an invertible function is one that has an inverse).
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