every analytic function is locally 1-1 whenever its derivative is nonzero): Let ?????C be open, and let...

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every analytic function is locally 1-1 whenever its derivative isnonzero): Let ?????Cbe open, and let ?:???f:??Cbe 1-1 and analytic on ? Then??(?0)?0f?(z0)?0for every ?0??z0??.
by contray suppose f'(z)=0

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