Questions: Multiply. √(-6) ⋅ √(-6) √(-6) ⋅ √(-6)= (Simplify your answer. Type your answer in the form a + bi. Type any radicals as needed.)

Solution Steps

To solve the problem of multiplying \(\sqrt{-6} \cdot \sqrt{-6}\), we need to recognize that we are dealing with complex numbers. The square root of a negative number involves the imaginary unit \(i\), where \(i = \sqrt{-1}\). Therefore, \(\sqrt{-6}\) can be expressed as \(\sqrt{6} \cdot i\). When multiplying two such terms, we use the property that \(i^2 = -1\).

1. Express \(\sqrt{-6}\) as \(\sqrt{6} \cdot i\).
2. Multiply \((\sqrt{6} \cdot i) \cdot (\sqrt{6} \cdot i)\).
3. Simplify using the property \(i^2 = -1\).

To multiply \(\sqrt{-6} \cdot \sqrt{-6}\), we first express \(\sqrt{-6}\) in terms of the imaginary unit \(i\). We have: \[ \sqrt{-6} = \sqrt{6} \cdot i \]

Next, we multiply the expressions: \[ (\sqrt{6} \cdot i) \cdot (\sqrt{6} \cdot i) = (\sqrt{6})^2 \cdot i^2 \]

Simplify the expression using the property \(i^2 = -1\): \[ (\sqrt{6})^2 \cdot i^2 = 6 \cdot (-1) = -6 \]

Final Answer