Multiply. \( \sqrt{-6} \cdot \sqrt{-7} \) \( \sqrt{-6} \cdot \sqrt{-7}=\square \) (Simplify your answer. Type your answer in the form a + bi. Type an exact answer, using radicals as needed.)

To multiply \( \sqrt{-6} \cdot \sqrt{-7} \), we can use the property of square roots that states: \[ \sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b} \] However, since both numbers are negative, we can express them in terms of imaginary numbers: \[ \sqrt{-6} = \sqrt{6} \cdot i \quad \text{and} \quad \sqrt{-7} = \sqrt{7} \cdot i \] Now we can multiply these two expressions: \[ \sqrt{-6} \cdot \sqrt{-7} = (\sqrt{6} \cdot i) \cdot (\sqrt{7} \cdot i) \] Using the associative property of multiplication, we can rearrange this as: \[ = \sqrt{6} \cdot \sqrt{7} \cdot i^2 \] Since \( i^2 = -1 \), we have: \[ = \sqrt{6} \cdot \sqrt{7} \cdot (-1) \] Now, we can simplify \( \sqrt{6} \cdot \sqrt{7} \): \[ \sqrt{6} \cdot \sqrt{7} = \sqrt{42} \] Thus, we can write: \[ \sqrt{-6} \cdot \sqrt{-7} = -\sqrt{42} \] In the form \( a + bi \), this can be expressed as: \[ 0 - \sqrt{42} = 0 - \sqrt{42}i \] So the final answer is: \[ \boxed{0 - \sqrt{42}i} \]