Express \( 4+\sqrt{-81} \) as a complex number \( 4+\sqrt{-81}=\square \)

To express \( 4 + \sqrt{-81} \) as a complex number, follow these steps: 1. **Understand the Square Root of a Negative Number:** \[ \sqrt{-81} = \sqrt{81 \times (-1)} = \sqrt{81} \times \sqrt{-1} = 9i \] Here, \( i \) is the imaginary unit, defined by \( i^2 = -1 \). 2. **Combine the Real and Imaginary Parts:** \[ 4 + \sqrt{-81} = 4 + 9i \] So, the complex number representation is: \[ 4 + \sqrt{-81} = 4 + 9i \] **Answer:** \( 4 + \sqrt{-81} = 4 + 9i \)