Complex number is complex

Algebra Level pending

\[ \ln(3+4i) = \dfrac AB \ln C + i \left(2n \pi + \arctan\left( \dfrac DE \right) \right) \]

If \(A,B,C,D\) and \(E\) are positive integers satisfying the equation above, with \( \gcd(A,B) = \gcd(D,E) = 1\), find \(A+B+C+E\).

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