Entire Function Bounded By Linear Function

Calculus Level 4

Suppose \(f: \mathbb{C} \to \mathbb{C}\) is holomorphic. Furthermore, assume \[|f(z)| \le 5|z|\] for all \(z\in \mathbb{C}\). If \(f(1) = 3+4i\), what is \(f(1+i)\)?

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