\[\large{\ln(3+4i) = A +Bi}\]

\(A\) and \(B\) are real numbers satisfying the equation above. Find the minimum value of \(A^2 + B^2\) to 2 decimal places.

**Notations:**

- \(i = \sqrt{-1}\) denotes the imaginary unit.
- \(\ln (\cdot)\) denotes the natural logarithm.

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