Entire Function Bounded By Linear Function

Calculus Level 3

Suppose f:CCf: \mathbb{C} \to \mathbb{C} is holomorphic. Furthermore, assume that

f(z)5z|f(z)| \le 5|z|

for all zCz\in \mathbb{C}. If f(1)=3+4if(1) = 3+4i, what is f(1+i)?f(1+i)?

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