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Let f C C, differentiable at the origin, f(0) = 0, and satisfy f(2z) = 2f(z) for all z = C. Prove that there

Let f C C, differentiable at the origin, f(0) = 0, and satisfy f(2z) = 2f(z) for all z = C. Prove that there exists c E C such that f(z) = cz for all z = C.

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