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Holomorphic Functions

If f(z) is holomorphic on |z|<1, f(0)=1, and for all |z|<=1 we have R(f(z))>=0, then show that -2<=R(f'(0))<=2

keywords: holomorphisms

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Holomorphic Functions are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.