Express \( 2+\sqrt{-9} \) as a complex number in the form \( a+b i \) \( 2+\sqrt{-9}=\square \)

To express \( 2 + \sqrt{-9} \) as a complex number in the form \( a + b i \), follow these steps: 1. **Understand the Components:** - The number \( 2 \) is the real part (\( a \)). - The term \( \sqrt{-9} \) involves the square root of a negative number, which relates to the imaginary unit \( i \), where \( i = \sqrt{-1} \). 2. **Simplify the Square Root of a Negative Number:** \[ \sqrt{-9} = \sqrt{9 \times (-1)} = \sqrt{9} \times \sqrt{-1} = 3i \] 3. **Combine the Real and Imaginary Parts:** \[ 2 + \sqrt{-9} = 2 + 3i \] 4. **Express in \( a + b i \) Form:** \[ 2 + \sqrt{-9} = 2 + 3i \] Here, \( a = 2 \) and \( b = 3 \). **Final Answer:** \[ 2 + \sqrt{-9} = 2 + 3i \]