# Complex Logarithm (Part 2)

$\large 3 \left[\ln \left(\frac{\sqrt{3}}{2} + \frac{1}{2}i\right) - \ln \left(\frac{\sqrt{3}}{2} - \frac{1}{2}i\right) \right] = A +Bi$

$A$ 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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