Multiply or divide, as indicated. Sim 1) \( \frac{\sqrt{-12} \cdot \sqrt{-3}}{\sqrt{4}} \)

To simplify the expression: \[ \frac{\sqrt{-12} \cdot \sqrt{-3}}{\sqrt{4}} \] we'll work with complex numbers, where \( i = \sqrt{-1} \). 1. **Simplify Each Square Root:** - \(\sqrt{-12} = \sqrt{12} \cdot i = 2\sqrt{3} \cdot i\) - \(\sqrt{-3} = \sqrt{3} \cdot i\) - \(\sqrt{4} = 2\) (since 4 is positive) 2. **Substitute Back into the Expression:** \[ \frac{(2\sqrt{3} \cdot i) \cdot (\sqrt{3} \cdot i)}{2} \] 3. **Multiply the Numerator:** \[ (2\sqrt{3} \cdot i) \cdot (\sqrt{3} \cdot i) = 2 \cdot 3 \cdot i^2 = 6i^2 \] Since \( i^2 = -1 \): \[ 6i^2 = 6(-1) = -6 \] 4. **Divide by the Denominator:** \[ \frac{-6}{2} = -3 \] **Final Answer:** \(-3\)